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Relevant bibliographies by topics / Groupe homotopie

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Academic literature on the topic 'Groupe homotopie'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 February 2022

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Journal articles on the topic "Groupe homotopie"

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Hempel, John. "One-relator surface groups." Mathematical Proceedings of the Cambridge Philosophical Society 108, no. 3 (1990): 467–74. http://dx.doi.org/10.1017/s030500410006936x.

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For X a subset of a group G, the smallest normal subgroup of G which contains X is called the normal closure of X and is denoted by ngp (X; G) or simply by ngp (X) if there is no possibility of ambiguity. By a surface group we mean the fundamental group of a compact surface. We are interested in determining when a normal subgroup of a surface group contains a simple loop – the homotopy class of an embedding of S1 in the surface, or more generally, a power of a simple loop. This is significant to the study of 3-manifolds since a Heegaard splitting of a 3-manifold is reducible (cf. [2]) if and only if the kernel of the corresponding splitting homomorphism contains a simple loop. We give an answer in the case that the normal subgroup is the normal closure ngp (α) of a single element α: if ngp (α) contains a (power of a) simple loop β then α is homotopic to a (power of a) simple loop and β±1 is homotopic either to (a power of) α or to the commutator [α, γ] of a with some simple loop γ meeting a transversely in a single point. This implies that if a is not homotopic to a power of a simple loop, then the quotient map π1(S) → π1(S)/ngp (α) does not factor through a group with more than one end. In the process we show that π1(S)/ngp (α) is locally indicable if and only if α is not a proper power and that α always lifts to a simple loop in the covering space Sα of S corresponding to ngp (α). We also obtain some estimates on the minimal number of double points in certain homotopy classes of loops.

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Rodriguez-Machin, Sergio. "Homotopy theories in additive categories are homotopies of Δ-groups". Rendiconti del Circolo Matematico di Palermo 39, № 1 (1990): 47–57. http://dx.doi.org/10.1007/bf02862876.

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Nicas, Andrew J. "An infinite family of non-Haken hyperbolic 3-manifolds with vanishing Whitehead groups." Mathematical Proceedings of the Cambridge Philosophical Society 99, no. 2 (1986): 239–46. http://dx.doi.org/10.1017/s030500410006415x.

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A manifold M is said to be aspherical if its universal covering space is contractible. Farrell and Hsiang have conjectured [3]:Conjecture A. (Topological rigidity of aspherical manifolds.) Any homotopy equivalence f: N → M between closed aspherical manifolds is homotopic to a homeomorphism,and its analogue in algebraic K-theory:Conjecture B. The Whitehead groups Whj(π1M)(j ≥ 0) of the fundamental group of a closed aspherical manifold M vanish.

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Theriault, Stephen D. "2-Primary Exponent Bounds for Lie Groups of Low Rank." Canadian Mathematical Bulletin 47, no. 1 (2004): 119–32. http://dx.doi.org/10.4153/cmb-2004-013-x.

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AbstractExponent information is proven about the Lie groups SU(3), SU(4), Sp(2), and G2 by showing some power of the H-space squaring map (on a suitably looped connected-cover) is null homotopic. The upper bounds obtained are 8, 32, 64, and 28 respectively. This null homotopy is best possible for SU(3) given the number of loops, off by at most one power of 2 for SU(4) and Sp(2), and off by at most two powers of 2 for G2.

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Møller, Jesper Michael. "Samelson Products In Spaces of Self-Homotopy Equivalences." Canadian Journal of Mathematics 42, no. 1 (1990): 95–108. http://dx.doi.org/10.4153/cjm-1990-006-7.

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The homotopy groups of any group-like space are equipped with a Samelson product satisfying, up to sign, the identities of a graded Lie bracket. We shall compute the Samelson product in two kinds of spaces of selfhomotopy equivalences arising when adding a homotopy or a homology group to a space.First, let A→ X be a cofibration with a Moore space M(G,n) as cofibre. For the monoid autA (X) of maps under A homotopic (rel. A) to the identity, the Samelson product is a pairingπn+i(G;X)⨂πn+j(G;X) → πn+i+j(G;X)of homotopy groups with coefficients [1] in G. Theorem 2.1 computes this pairing in terms of a homomorphism associated to a α ∈ πi(autAX)).

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Bagchi, Susmit. "Connected Fundamental Groups and Homotopy Contacts in Fibered Topological (C, R) Space." Symmetry 13, no. 3 (2021): 500. http://dx.doi.org/10.3390/sym13030500.

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The algebraic as well as geometric topological constructions of manifold embeddings and homotopy offer interesting insights about spaces and symmetry. This paper proposes the construction of 2-quasinormed variants of locally dense p-normed 2-spheres within a non-uniformly scalable quasinormed topological (C, R) space. The fibered space is dense and the 2-spheres are equivalent to the category of 3-dimensional manifolds or three-manifolds with simply connected boundary surfaces. However, the disjoint and proper embeddings of covering three-manifolds within the convex subspaces generates separations of p-normed 2-spheres. The 2-quasinormed variants of p-normed 2-spheres are compact and path-connected varieties within the dense space. The path-connection is further extended by introducing the concept of bi-connectedness, preserving Urysohn separation of closed subspaces. The local fundamental groups are constructed from the discrete variety of path-homotopies, which are interior to the respective 2-spheres. The simple connected boundaries of p-normed 2-spheres generate finite and countable sets of homotopy contacts of the fundamental groups. Interestingly, a compact fibre can prepare a homotopy loop in the fundamental group within the fibered topological (C, R) space. It is shown that the holomorphic condition is a requirement in the topological (C, R) space to preserve a convex path-component. However, the topological projections of p-normed 2-spheres on the disjoint holomorphic complex subspaces retain the path-connection property irrespective of the projective points on real subspace. The local fundamental groups of discrete-loop variety support the formation of a homotopically Hausdorff (C, R) space.

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Hajłasz, Piotr, Armin Schikorra, and Jeremy T. Tyson. "Homotopy Groups of Spheres and Lipschitz Homotopy Groups of Heisenberg Groups." Geometric and Functional Analysis 24, no. 1 (2014): 245–68. http://dx.doi.org/10.1007/s00039-014-0261-z.

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Biedermann, Georg, and William G. Dwyer. "Homotopy nilpotent groups." Algebraic & Geometric Topology 10, no. 1 (2010): 33–61. http://dx.doi.org/10.2140/agt.2010.10.33.

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Ghane, H., Z. Hamed, B. Mashayekhy, and H. Mirebrahimi. "Topological Homotopy Groups." Bulletin of the Belgian Mathematical Society - Simon Stevin 15, no. 3 (2008): 455–64. http://dx.doi.org/10.36045/bbms/1222783092.

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Moller, Jesper M. "Homotopy Lie Groups." Bulletin of the American Mathematical Society 32, no. 4 (1995): 413–29. http://dx.doi.org/10.1090/s0273-0979-1995-00613-0.

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Dissertations / Theses on the topic "Groupe homotopie"

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Dousson, Xavier. "Homologie effective des classifiants et calculs de groupes d'homotopie." Université Joseph Fourier (Grenoble), 1999. http://www.theses.fr/1999GRE10170.

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Ce memoire etudie certaines methodes de topologie algebrique constructive, visant notamment le calcul des groupes d'homotopie. Il s'agit de developper, pour les rendre constructifs, les outils classiques de la topologie algebrique. La realisation sur machine des tours de postnikov et whitehead est alors possible. Les ingredients essentiels pour ces tours sont les espaces d'eilenberg-maclane et les fibrations. Ce memoire est donc pour l'essentiel consacre a : - l'homologie effective de la deuxieme suite spectrale d'eilenberg-moore. Une version effective de cette deuxieme suite spectrale est definie, puis utilisee ; plus generalement le calcul de l'homologie effective des espaces classifiants des groupes simpliciaux est obtenu. - une version effective de la suite spectrale de serre. Ce travail a conduit en particulier a l'ecriture d'un programme clos (le systeme objet common lisp) de topologie algebrique constructive : le logiciel kenzo.

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Quemel, Taísa Fernanda de Lima [UNESP]. "Homotopias e aplicações." Universidade Estadual Paulista (UNESP), 2016. http://hdl.handle.net/11449/136229.

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Submitted by TAÍSA FERNANDA DE LIMA QUEMEL null (taisafernanda.10@hotmail.com) on 2016-03-10T20:25:22Z No. of bitstreams: 1 Versão final_Dissertação_Taísa Quemel.pdf: 674351 bytes, checksum: 3498053a8bb53e50ac3119a10d45a0c5 (MD5)<br>Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-03-11T12:17:58Z (GMT) No. of bitstreams: 1 quemel_tfl_me_sjrp.pdf: 674351 bytes, checksum: 3498053a8bb53e50ac3119a10d45a0c5 (MD5)<br>Made available in DSpace on 2016-03-11T12:17:58Z (GMT). No. of bitstreams: 1 quemel_tfl_me_sjrp.pdf: 674351 bytes, checksum: 3498053a8bb53e50ac3119a10d45a0c5 (MD5) Previous issue date: 2016-02-26<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>O objetivo deste trabalho é mostrar que πn(X) é sempre abeliano quando n ≥ 2 e que π1(X) é abeliano quando X for um H-espaço e por fim calcular alguns grupos de homotopia utilizando sequência exata de uma fibração.<br>The goal of this work is to show that πn(X) is always abelian when n ≥ 2 and that π1(X) is abelian when X is an H-space and finally calculate some homotopy groups using the exact sequence of a fibration.

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Aubriot, Thomas. "Classification des objets galoisiens d'une algèbre de Hopf." Phd thesis, Université Louis Pasteur - Strasbourg I, 2007. http://tel.archives-ouvertes.fr/tel-00151368.

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Cette thèse porte sur la classification des objets galoisiens d'une algèbre de Hopf. Le concept d'extension de Hopf-Galois, qui a été beaucoup étudié ces dernières années, est une généralisation du concept d'extension galoisienne de corps, mais aussi un analogue des fibrés principaux dans le cadre de la géométrie non commutative. Si $H$ est une algèbre de Hopf, une algèbre $H$-comodule $(Z,\delta: Z \to Z \otimes H)$ est une $H$-extension de Hopf-Galois d'une sous-algèbre $B\subset Z$ si l'ensemble des éléments co\"\i nvariants de $Z$ co\"\i ncide avec $B$ et si l'application canonique $\beta : Z \otimes _B Z \to Z\otimes H$ définie par <br />$$ \beta (x\otimes y ) = \delta (x) (y\otimes 1)$$ est une bijection. Les objets galoisiens forment une classe importante d'extensions de Hopf-Galois ; ce sont celles dont la sous-algèbre des co\"\i nvariants se réduit à l'anneau de base. Bien qu'une littérature abondante ait été consacrée aux extensions de Hopf-Galois, on a peu de résultats sur leur classification à isomorphisme près. Pour contourner la difficulté de classer les extensions de Hopf-Galois à isomorphisme près, Kassel a introduit et développé avec Schneider une relation d'équivalence sur les extensions de Hopf-Galois qu'il a appelée homotopie. <br /><br />Dans cette thèse nous donnons des résultats de classification à homotopie et à isomorphisme près. Notre approche de la classification des objets galoisiens tourne autour de trois axes. <br />\begin{itemize} <br />\item[a)] La construction explicite de représentants des classes d'homotopie des objets galoisiens de l'algèbre $U_q(\mathfrak{g})$ associée par Drinfeld et Jimbo à une algèbre de Lie $\mathfrak{g}$, explicitant ainsi un théorème de Kassel et Schneider. <br />\item[b)] Une étude des objets galoisiens de l'alg\` ebre quantique $O_q (SL(2))$ des fonctions sur le groupe $SL (2)$, et donc un résultat de classification en dimension infinie; nous donnons la classification à isomorphisme près et des résultats partiels pour la classification à homotopie près. <br />\item[c)] Une étude systématique de la classification à isomorphisme et à homotopie près pour les algèbres de Hopf de dimension $\leq 15$ ; nous synthétisons des résultats éparpillés dans la littérature, portant sur des familles d'algèbres de Hopf pointées ou semisimples et nous complétons ces résultats en donnant la classification des objets galoisiens d'une algèbre de Hopf de dimension $8$ qui n'est ni semisimple ni <br />pointée. <br />\end{itemize}

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Lader, Olivier. "Une résolution projective pour le second groupe de Morava pour p ≥ 5 et applications." Phd thesis, Université de Strasbourg, 2013. http://tel.archives-ouvertes.fr/tel-00875761.

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Dans les années 80, Shimomura a déterminé les groupes d'homotopie du spectre de Moore V(0) localisé par rapport à K(2) la deuxième K-théorie de Morava. Plus tard, avec les travaux de Devinatz et Hopkins est apparu une autre suite spectrale convergeant vers les précédents groupes d'homotopies. Lorsque le paramètre premier p de la théorie K(2) est supérieur ou égal à cinq, la précédente suite spectrale dégénère. Ainsi, déterminer ces groupes d'homotopie revient à calculer les groupes de cohomologie du groupe stabilisateur de Morava à coefficients dans l'anneau de Lubin-Tate modulo p. En 2007, Henn a démontré l'existence, lorsque p > 3, d'une résolution projective du groupe de Morava de longueur quatre. Dans cette thèse, nous précisons une telle résolution projective. On l'applique ensuite au calcul effectif des groupes de cohomologie à coefficients dans l'anneau de Lubin-Tate modulo p. Enfin, on donne une seconde application, en redémontrant un résultat de Hopkins non publié sur le groupe de Picard de la catégorie des spectres K(2)-locaux.

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Silva, Luciana Vale. "Teoria de homotopia simples e torção de Whitehead." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-18062007-143128/.

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Este trabalho apresenta a teoria de homotopia simples, desenvolvida por J. H. C. Whitehead, com o objetivo de obter um método para classificar espaços com o mesmo tipo de homotopia. Com esta motivação, Whitehead introduz o conceito de equivalência de homotopia simples entre complexos simpliciais, que posteriormente é generalizado para complexos CW, espaços criados pelo próprio Whitehead. Um resultado imediato desta teoria é que quando dois espaços têm o mesmo tipo de homotopia simples, eles têm o mesmo tipo de homotopia. A recíproca desta afirmação é então conjecturada. Mostraremos que trata-se de uma conjectura falsa, contudo a investigação de sua confirmação produz um material que toma rumo próprio. Nosso enfoque são os aspectos algébricos envolvidos nesta investigação<br>This work presents the simple-homotopy theory, developed by J. H. C. Whitehead, with the goal to get an method to classify spaces with the same homotopy type. So, with this motivation, Whitehead introduced the concept of simple-homotopy equivalence between simplicial complexes, that later was generalized for CW complexes, spaces created by himself. An immediate result of this theory is that, if two spaces have the same simple-homotopy type, they have the same homotopy type. Then, the reciprocal statement is conjectured. We will show that the conjecture is not true, but the research about its truthfulness produces a material that takes its own way. Our approach are the algebraic aspects involved in this research

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Peterson, Aaron. "Pipe diagrams for Thompson's Group F /." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1959.pdf.

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Junior, Luiz Roberto Hartmann. "Homotopia simples e classificação dos espaços lenticulares." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-03052007-104226/.

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Fizemos uma apresentação detalhada, com um enfoque geométrico, da Teoria de Homotopia Simples e como aplicação, uma análise detalhada da classificação por homotopia e homotopia simples dos Espaços Lenticulares<br>We made a detailed presentation, with a geometric approach, of Simple Homotopy Theory and as a major application we present a detailed analysis of homotopy and simple homotopy classification of Lens Spaces

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Manin, Fedor. "Asymptotic invariants of homotopy groups." Thesis, The University of Chicago, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3712650.

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<p> We study the homotopy groups of a finite CW complex <i>X</i> via constraints on the geometry of representatives of their elements. For example, one can measure the “size” of α ∈ π<i> n</i> (<i>X</i>) by the optimal Lipschitz constant or volume of a representative. By comparing the geometrical structure thus obtained with the algebraic structure of the group, one can define functions such as growth and distortion in π<i>n</i>(<i>X</i>), analogously to the way that such functions are studied in asymptotic geometric group theory.</p><p> We provide a number of examples and techniques for studying these invariants, with a special focus on spaces with few rational homotopy groups. Our main theorem characterizes those <i>X</i> in which all non-torsion homotopy classes are undistorted, that is, their volume distortion functions, and hence also their Lipschitz distortion functions, are linear.</p>

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Klaus, Michele. "Group actions on homotopy spheres." Thesis, University of British Columbia, 2011. http://hdl.handle.net/2429/35981.

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In the first part of the thesis we discuss the rank conjecture of Benson and Carlson. In particular, we prove that if G is a finite p-group of rank 3 and with p odd, or if G is a central extension of abelian p-groups, then there is a free finite G-CW-complex homotopy equivalent to the product of rk(G) spheres; where rk(G) is the rank of G. We also treat an extension of the rank conjecture to groups of finite virtual cohomological dimension. In this context, for p a fixed odd prime, we show that there is an infinite group L satisfying the two following properties: every finite subgroup G<L is a p-group with rk(G)<3 and for every finite dimensional L-CW-complex homotopy equivalent to a sphere, there is at least one isotropy subgroup H<L with rk(H)=2. In the second part of the thesis we discuss the study of homotopy G-spheres up to Borel equivalence. In particular, we provide a new approach to the construction of finite homotopy G-spheres up to Borel equivalence, and we apply it to give some new examples for some semi-direct products.

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Claudio, Mario Henrique Andrade. "Tipos de homotopia dos grupos de gauge dos fibrados linhas quaterniônicos sobre esferas." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-02072008-140307/.

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Seja p um \'S POT. 3\' - fibrado principal sobre uma esfera \'S POT. n\' , com n \' >OU=\' 4 . O objetivo deste trabalho é calcular os tipos de homotopia do grupo de gauge \'G IND. p\' desses fibrados p, estendendo o resultado determinado por A. Kono [25] quando n = 4. Apresentamos fórmulas explícitas para o operador bordo na seqüência exata de homotopia associada com a aplicação avaliação ev : m(\'S POT. n\' , B \'S POT. 3\' ) \'SETA\' B \'S POT. 3\' , traduzindo o problema nos cálculos envolvendo grupos de homotopia de esferas. Calculamos todos os casos clássicos, ou seja, aqueles que podem ser avaliados usando as informações encontradas no livro de H. Toda [46], determinando o tipo de homotopia do grupo de gauge desses fibrados para cada n \' > OU =\' 25<br>Let p be a principal \'S POT. 3\' - bundle over a sphere \'S POT. n\' , with n\' > or =\' 4\'. The subject of this work is to calculate the homotopy type of the gauge group \'G IND. p\' of these bundles p, extending the result determined by A. Kono [25] when n = 4. We present explicit formulas for the boundary operator in the homotopy exact sequence associated with the evaluation map ev : m(\'S POT. n\' , B \'S POT. 3\' ) \' ARROW\' B \'S POT. 3\' , translating that problem into calculations involving homotopy groups of sphere. We calculate all the classical cases, namely those that can be dealt with using the information in the book of H. Toda [46], determining the homotopy type of the gauge group of these bundles for each n \'> or = 25

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Books on the topic "Groupe homotopie"

1

Mimura, M. Topology of lie groups, I and II. American Mathematical Society, 1991.

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lix, Y. Fe. La dichotomie elliptique-hyperbolique en homotopie rationnelle. Socie te mathe matique de France, 1989.

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Félix, Y. La dichotomie elliptique-hyperbolique en homotopie rationnelle. Société mathématique de France, 1989.

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lix, Y. Fe. La dichotomie elliptique-hyperbolique en homotopie rationnelle. Socie te Mathe matique de France, 1989.

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Félix, Y. La dichotomie elliptique-hyperbolique en homotopie rationnelle. Société mathématique de France, 1989.

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Kochman, Stanley O. Stable Homotopy Groups of Spheres. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0083795.

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Levi, Ran. On finite groups and homotopy theory. American Mathematical Society, 1995.

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Aguadé, Jaume, Manuel Castellet, and Frederick Ronald Cohen, eds. Algebraic Topology Homotopy and Group Cohomology. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0087495.

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Dwyer, William G., and Hans-Werner Henn. Homotopy Theoretic Methods in Group Cohomology. Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8356-6.

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Collins, E. A homotopy algorithm for digital optimal projection control, GASD-HADOC. Harris Corp., Government Aerospace System Division, 1993.

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Book chapters on the topic "Groupe homotopie"

1

Johnson, F. E. A. "Group Rings of Cyclic Groups." In Syzygies and Homotopy Theory. Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-2294-4_10.

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Johnson, F. E. A. "Group Rings of Dihedral Groups." In Syzygies and Homotopy Theory. Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-2294-4_11.

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Johnson, F. E. A. "Group Rings of Quaternion Groups." In Syzygies and Homotopy Theory. Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-2294-4_12.

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Crossley, Martin D. "Homotopy Groups." In Springer Undergraduate Mathematics Series. Springer London, 2010. http://dx.doi.org/10.1007/1-84628-194-6_8.

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Aguilar, Marcelo, Samuel Gitler, and Carlos Prieto. "Homotopy Groups." In Universitext. Springer New York, 2002. http://dx.doi.org/10.1007/0-387-22489-0_3.

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Dubrovin, B. A., S. P. Novikov, and A. T. Fomenko. "Homotopy Groups." In Graduate Texts in Mathematics. Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4612-1100-6_5.

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Naber, Gregory L. "Homotopy Groups." In Topology, Geometry, and Gauge Fields. Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4757-2742-5_3.

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Naber, Gregory L. "Homotopy Groups." In Texts in Applied Mathematics. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-7254-5_2.

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Schwarz, Albert S. "Homotopy Groups." In Grundlehren der mathematischen Wissenschaften. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-662-02998-5_9.

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Ferrario, Davide L., and Renzo A. Piccinini. "Homotopy Groups." In CMS Books in Mathematics. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-7236-1_6.

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Conference papers on the topic "Groupe homotopie"

1

Cohen, Frederick, and Jie Wu. "On braid groups and homotopy groups." In Groups, homotopy and configuration spaces, in honour of Fred Cohen's 60th birthday. Mathematical Sciences Publishers, 2008. http://dx.doi.org/10.2140/gtm.2008.13.169.

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Devinatz, Ethan S. "Homotopy groups of homotopy fixed point spectra associated to En." In International Conference in Homotopy Theory. Mathematical Sciences Publishers, 2007. http://dx.doi.org/10.2140/gtm.2007.10.131.

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Cohen, F. R., and J. Pakianathan. "The stable braid group and the determinant of the Burau representation." In International Conference in Homotopy Theory. Mathematical Sciences Publishers, 2007. http://dx.doi.org/10.2140/gtm.2007.10.117.

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Ishiguro, Kenshi. "Classifying spaces of compact Lie groups that are p–compact for all prime numbers." In International Conference in Homotopy Theory. Mathematical Sciences Publishers, 2007. http://dx.doi.org/10.2140/gtm.2007.10.195.

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Buchholtz, Ulrik, Floris van Doorn, and Egbert Rijke. "Higher Groups in Homotopy Type Theory." In LICS '18: 33rd Annual ACM/IEEE Symposium on Logic in Computer Science. ACM, 2018. http://dx.doi.org/10.1145/3209108.3209150.

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Golasiński, Marek, Daciberg L. Gonçalves, and Peter N. Wong. "A note on generalized equivariant homotopy groups." In Algebraic Topology - Old and New. Institute of Mathematics Polish Academy of Sciences, 2009. http://dx.doi.org/10.4064/bc85-0-12.

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Kraus, Nicolai, and Thorsten Altenkirch. "Free Higher Groups in Homotopy Type Theory." In LICS '18: 33rd Annual ACM/IEEE Symposium on Logic in Computer Science. ACM, 2018. http://dx.doi.org/10.1145/3209108.3209183.

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Kameko, Masaki, and Mamoru Mimura. "On the Rothenberg–Steenrod spectral sequence for the mod 3 cohomology of the classifying space of the exceptional Lie group E8." In International Conference in Homotopy Theory. Mathematical Sciences Publishers, 2007. http://dx.doi.org/10.2140/gtm.2007.10.213.

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Palmeira, Eduardo S., and Benjamin R. C. Bedregal. "On F-homotopy and F-fundamental group." In NAFIPS 2011 - 2011 Annual Meeting of the North American Fuzzy Information Processing Society. IEEE, 2011. http://dx.doi.org/10.1109/nafips.2011.5751921.

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Abbaspour, Hossein, Ralph Cohen, and Kate Gruher. "String topology of Poincaré duality groups." In Groups, homotopy and configuration spaces, in honour of Fred Cohen's 60th birthday. Mathematical Sciences Publishers, 2008. http://dx.doi.org/10.2140/gtm.2008.13.1.

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