Relevant bibliographies by topics / Homotopy

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Homotopy'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Homotopy"

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Pan, Binfeng, Xun Pan, and Yangyang Ma. "A quadratic homotopy method for fuel-optimal low-thrust trajectory design." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 5 (2018): 1741–57. http://dx.doi.org/10.1177/0954410018761965.

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Solving fuel-optimal low-thrust trajectory problems is a long-standing challenging topic, mainly due to the existence of discontinuous bang–bang controls and small convergence domain. Homotopy methods, the principle of which is to embed a given problem into a family of problems parameterized by a homotopic parameter, have been widely applied to address this difficulty. Linear homotopy methods, the homotopy functions of which are linear functions of the homotopic parameter, serve as useful tools to provide continuous optimal controls during the homotopic procedure with an energy-optimal low-thr
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Kareem, Azhar. "Fuzzy Relative Homotopy and Fuzzy Weak Equivalence with Some Results." Wasit Journal for Pure sciences 3, no. 3 (2024): 9–15. http://dx.doi.org/10.31185/wjps.431.

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In this paper, first introduce my concept fuzzy homotopic and fuzzy homotopic relative and weproved that the relation fuzzy homotopic relative is a fuzzy equivalence relation. Secondly , weintroduce the concepts fuzzy homotopy equivalence, fuzzy fundamental group and fuzzy weak homotopy equivalence. We have proven some important theorems.
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Koceić-Bilan, Nikola, and Ivančica Mirošević. "On classification of morphisms by box-homotopy." Acta mathematica Spalatensia 1, no. 1 (2021): 97–103. http://dx.doi.org/10.32817/ams.1.1.8.

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In [1] the authors proposed a generalization of the notion of homotopy, a relation called to be box-homotopic, proven to be an equivalence relation on Top(X,Y) and well-adjusted with the composition. In this article we prove that all the mappings of Top(X,Y) are box-homotopic, that is, the classification of morphisms by the box-homotopy relation is the coarsest.
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Staecker, P. Christopher. "Digital homotopy relations and digital homology theories." Applied General Topology 22, no. 2 (2021): 223. http://dx.doi.org/10.4995/agt.2021.13154.

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In this paper we prove results relating to two homotopy relations and four homology theories developed in the topology of digital images.<br /><br />We introduce a new type of homotopy relation for digitally continuous functions which we call ``strong homotopy.'' Both digital homotopy and strong homotopy are natural digitizations of classical topological homotopy: the difference between them is analogous to the difference between digital 4-adjacency and 8-adjacency in the plane.<br /><br />We also consider four different digital homology theories: a simplicial homology
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Side, Syafruddin, Maya Sari Wahyuni, and Muh Rifki. "Solusi Numerik Model SIR pada Penyebaran Penyakit Hepatitis B dengan Metode Perturbasi Homotopi di Provinsi Sulawesi Selatan." Journal of Mathematics, Computations, and Statistics 3, no. 2 (2020): 79. http://dx.doi.org/10.35580/jmathcos.v3i2.20122.

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Penelitian ini membahas mengenai solusi secara numerik dari model SIR pada penyebaran penyakit Hepatitis B dengan Metode Perturbasi Homotopi. Data yang digunakan adalah data sekunder dari penelitian Rosdiana (2015) yang berupa model SIR dan jumlah penderita Hepatitis B di Provinsi Sulawesi Selatan tahun 2015 dari Dinas Kesehatan Provinsi Sulawesi Selatan. Pembahasan dimulai dari penentuan solusi umum dengan Metode Perturbasi Homotopi, penentuan parameter, simulasi dan analisis hasil. Setelah dilakukan analisis dari simulasi numerik terlihat bahwa Metode Perturbasi Homotopi dapat digunakan untu
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Kazemi-Baneh, M. Z. "Homotopic Chain Maps Have Equals-Homology andd-Homology." International Journal of Mathematics and Mathematical Sciences 2016 (2016): 1–5. http://dx.doi.org/10.1155/2016/5647548.

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The homotopy of chain maps on preabelian categories is investigated and the equality of standard homologies andd-homologies of homotopic chain maps is established. As a special case, ifXandYare the same homotopy type, then theirnthd-homologyR-modules are isomorphic, and ifXis a contractible space, then itsnthd-homologyR-modules forn≠0are trivial.
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Lyubashenko, V., and A. Matsui. "Homotopy equivalence of normalized and unnormalized complexes, revisited." Algebra and Discrete Mathematics 32, no. 2 (2021): 253–66. http://dx.doi.org/10.12958/adm1879.

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We consider the unnormalized and normalized complexes of a simplicial or a cosimplicial object coming from the Dold-Kan correspondence for an idempotent complete additive category (kernels and cokernels are not required). The normalized complex is defined as the image of certain idempotent in the unnormalized complex. We prove that this idempotent is homotopic to identity via homotopy which is expressed via faces and degeneracies. Hence, the normalized and unnormalized complex are homotopy isomorphic to each other. We provide explicit formulae for the homotopy.
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FIEDLER, THOMAS, and ARNAUD MORTIER. "ON HOMOTOPIES WITH TRIPLE POINTS OF CLASSICAL KNOTS." Journal of Knot Theory and Its Ramifications 21, no. 04 (2012): 1250038. http://dx.doi.org/10.1142/s0218216511009911.

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We consider a knot homotopy as a cylinder in 4-space. An ordinary triple point p of the cylinder is called coherent if all three branches intersect at p pairwise with the same intersection index. A triple unknotting of a classical knot K is a homotopy which connects K with the trivial knot and which has as singularities only coherent triple points. We give a new formula for the first Vassiliev invariant v2(K) by using triple unknottings. As a corollary we obtain a very simple proof of the fact that passing a coherent triple point always changes the knot type. As another corollary we show that
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Dyer, Eldon, and Joseph Roitberg. "Homotopy-epimorphisms, homotopy-monomorphisms and homotopy-equivalences." Topology and its Applications 46, no. 2 (1992): 119–24. http://dx.doi.org/10.1016/0166-8641(92)90127-l.

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Kang, Min, and Sang-Eon Han. "Compression of Khalimsky topological spaces." Filomat 26, no. 6 (2012): 1101–14. http://dx.doi.org/10.2298/fil1206101k.

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Aiming at the study of the compression of Khalimsky topological spaces which is an interesting field in digital geometry and computer science, the present paper develops a new homotopy thinning suitable for the work. Since Khalimsky continuity of maps between Khalimsky topological spaces has some limitations of performing a discrete geometric transformation, the paper uses another continuity (see Definition 3.4) that can support the discrete geometric transformation and a homotopic thinning suitable for studying Khalimsky topological spaces. By using this homotopy, we can develop a new homotop
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Dissertations / Theses on the topic "Homotopy"

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Grbić, Jelena. "Universal homotopy associative, homotopy commutative H-spaces." Thesis, University of Aberdeen, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.401586.

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For any connected space <i>X</i> the James construction shows that Ω<span style='font-family:Symbol'>S<i>X</i> is universal in the category of homotopy associative <i>H</i>-spaces in the sense that any map <i>f</i>: <i>X </i><i><span style='font-family:Symbol'>® Y </i>to a homotopy associative <i>H</i>-space factors through a uniquely determined H-map. Let <i>p</i> be a fixed prime number, and <i>X</i> a space localised at <i>p</i>.  We study the possibility of generating a universal space <i>U(X)</i> from <i>X</i> which is universal in the category of homotopy associative, homotopy commutativ
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Saleh, Bashar. "Formality and homotopy automorphisms in rational homotopy theory." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-160835.

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This licentiate thesis consists of two papers treating subjects in rational homotopy theory. In Paper I, we establish two formality conditions in characteristic zero. We prove that adg Lie algebra is formal if and only if its universal enveloping algebra is formal. Wealso prove that a commutative dg algebra is formal as a dg associative algebra if andonly if it is formal as a commutative dg algebra. We present some consequences ofthese theorems in rational homotopy theory. In Paper II, we construct a differential graded Lie model for the universal cover of the classifying space of the grouplik
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Rehmeyer, Julie. "Homotopy colimits." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/42605.

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Szumiło, Karol [Verfasser]. "Two Models for the Homotopy Theory of Cocomplete Homotopy Theories / Karol Szumiło." Bonn : Universitäts- und Landesbibliothek Bonn, 2014. http://d-nb.info/1238687156/34.

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Fleming, Thomas R. "Generalized link homotopy invariants." Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2006. http://wwwlib.umi.com/cr/ucsd/fullcit?p3208096.

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Thesis (Ph. D.)--University of California, San Diego, 2006.<br>Title from first page of PDF file (viewed June 2, 2006). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 72-75).
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Wang, Guozhen Ph D. Massachusetts Institute of Technology. "Unstable chromatic homotopy theory." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/99321.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 57-58).<br>In this thesis, I study unstable homotopy theory with chromatic methods. Using the v, self maps provided by the Hopkins-Smith periodicity theorem, we can decompose the unstable homotopy groups of a space into its periodic parts, except some lower stems. For fixed n, using the Bousfield-Kuhn functor [Phi]n, we can associate to any space a spectrum, which captures the vo-periodic part of its homotopy groups. I st
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Beke, Tibor 1970. "Homotopy theory and topoi." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/47465.

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Douglas, Christopher L. "Twisted stable homotopy theory." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/33095.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.<br>Includes bibliographical references (p. 133-137).<br>There are two natural interpretations of a twist of stable homotopy theory. The first interpretation of a twist is as a nontrivial bundle whose fibre is the stable homotopy category. This kind of radical global twist forms the basis for twisted parametrized stable homotopy theory, which is introduced and explored in Part I of this thesis. The second interpretation of a twist is as a nontrivial bundle whose fibre is a particular element in the stable homoto
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Quirin, Kevin. "Lawvere-Tierney sheafification in Homotopy Type Theory." Thesis, Nantes, Ecole des Mines, 2016. http://www.theses.fr/2016EMNA0298/document.

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Le but principal de cette thèse est de définir une extension de la traduction de double-négation de Gödel à tous les types tronqués, dans le contexte de la théorie des types homotopique. Ce but utilisera des théories déjà existantes, comme la théorie des faisceaux de Lawvere-Tierney, quenous adapterons à la théorie des types homotopiques. En particulier, on définira le fonction de faisceautisation de Lawvere-Tierney, qui est le principal théorème présenté dans cette thèse.Pour le définir, nous aurons besoin de concepts soit déjà définis en théorie des types, soit non existants pour l’instant.
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Su, Zhixu. "Rational homotopy type of manifolds." [Bloomington, Ind.] : Indiana University, 2009. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3378383.

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Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2009.<br>Title from PDF t.p. (viewed on Jul 9, 2010). Source: Dissertation Abstracts International, Volume: 70-10, Section: B, page: 6263. Adviser: James F. Davis.
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Books on the topic "Homotopy"

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1947-, Porter T., ed. Abstract homotopy and simple homotomy theory. World Scientific, 1997.

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Kamps, Klaus Heiner. Abstract homotopy and simple homotopy theory. World Scientific, 1997.

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Heller, Alex. Homotopy theories. American Mathematical Society, 1988.

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Baues, Hans J. Algebraic homotopy. Cambridge University Press, 1989.

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Dundas, Bjørn Ian, Marc Levine, Paul Arne Østvær, Oliver Röndigs, and Vladimir Voevodsky, eds. Motivic Homotopy Theory. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-45897-5.

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Wen-tsün, Wu. Rational Homotopy Type. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0081997.

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Félix, Yves, Stephen Halperin, and Jean-Claude Thomas. Rational Homotopy Theory. Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0105-9.

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Jardine, John F. Local Homotopy Theory. Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4939-2300-7.

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Goerss, Paul G., and John F. Jardine. Simplicial Homotopy Theory. Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-0346-0189-4.

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Goerss, Paul G., and John F. Jardine. Simplicial Homotopy Theory. Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8707-6.

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Book chapters on the topic "Homotopy"

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Rutter, John W. "Homotopy type, homotopy groups." In Spaces of Homotopy Self-Equivalences. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0093755.

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Crossley, Martin D. "Homotopy." In Springer Undergraduate Mathematics Series. Springer London, 2010. http://dx.doi.org/10.1007/1-84628-194-6_6.

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Manetti, Marco. "Homotopy." In UNITEXT. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16958-3_10.

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Strom, Jeffrey. "Homotopy." In Graduate Studies in Mathematics. American Mathematical Society, 2011. http://dx.doi.org/10.1090/gsm/127/04.

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Manetti, Marco. "Homotopy." In UNITEXT. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-32142-9_10.

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Kinsey, L. Christine. "Homotopy." In Topology of Surfaces. Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0899-0_9.

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Parthasarathy, K. "Homotopy." In UNITEXT. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-9484-4_14.

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Vassiliev, V. "Homotopy groups and homotopy equivalence." In The Student Mathematical Library. American Mathematical Society, 2001. http://dx.doi.org/10.1090/stml/014/02.

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Hinich, V. A., and V. V. Schechtman. "On homotopy limit of homotopy algebras." In K-Theory, Arithmetic and Geometry. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0078370.

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Hardie, K. A., and K. H. Kamps. "The Homotopy category of homotopy factorizations." In Algebraic Topology Barcelona 1986. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0083008.

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Conference papers on the topic "Homotopy"

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Pardis, Shayan, Matthew Chignoli, and Sangbae Kim. "Probabilistic Homotopy Optimization for Dynamic Motion Planning." In 2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2024. https://doi.org/10.1109/iros58592.2024.10802528.

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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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Badiger, Chidanand, and T. Venkatesh. "Generalised (g) homotopy and generalised (g) homotopy type spaces." In 4TH INTERNATIONAL CONFERENCE ON THE SCIENCE AND ENGINEERING OF MATERIALS: ICoSEM2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0028740.

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Furuta, Mikio, Yukio Kametani, Hirofumi Matsue, and Norihiko Minami. "Homotopy theoretical considerations of the Bauer–Furuta stable homotopy Seiberg–Witten invariants." In International Conference in Homotopy Theory. Mathematical Sciences Publishers, 2007. http://dx.doi.org/10.2140/gtm.2007.10.155.

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Rodrigo, Rodolfo H., Daniel H. Patino, and Gustavo Schweickardt. "Neuronal Homotopy Regressors." In 2021 XIX Workshop on Information Processing and Control (RPIC). IEEE, 2021. http://dx.doi.org/10.1109/rpic53795.2021.9648481.

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Prieto-Cubides, Jonathan. "On homotopy of walks and spherical maps in homotopy type theory." In CPP '22: 11th ACM SIGPLAN International Conference on Certified Programs and Proofs. ACM, 2022. http://dx.doi.org/10.1145/3497775.3503671.

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Behrens, Mark. "Some root invariants at the prime 2." In International Conference in Homotopy Theory. Mathematical Sciences Publishers, 2007. http://dx.doi.org/10.2140/gtm.2007.10.1.

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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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Furuta, Mikio, Yukio Kametani, and Norihiko Minami. "Nilpotency of the Bauer–Furuta stable homotopy Seiberg–Witten invariants." In International Conference in Homotopy Theory. Mathematical Sciences Publishers, 2007. http://dx.doi.org/10.2140/gtm.2007.10.147.

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Hemmi, Yutaka, and Yusuke Kawamoto. "Higher homotopy commutativity and cohomology of finite H–spaces." In International Conference in Homotopy Theory. Mathematical Sciences Publishers, 2007. http://dx.doi.org/10.2140/gtm.2007.10.167.

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Reports on the topic "Homotopy"

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Dunlavy, Daniel M., and Dianne P. O'Leary. Homotopy optimization methods for global optimization. Office of Scientific and Technical Information (OSTI), 2005. http://dx.doi.org/10.2172/876373.

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Myers, Nicholas T., and James S. Warsa. Application of Homotopy Continuation to SN Transport Applications. Office of Scientific and Technical Information (OSTI), 2013. http://dx.doi.org/10.2172/1090633.

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Watson, Layne T. Homotopy Methods in Control System Design and Analysis. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada251641.

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Gurdal, Zafer, Raphael T. Haftka, and Layne T. Watson. Wing Structural Design by Genetic Algorithms and Homotopy Methods. Defense Technical Information Center, 1999. http://dx.doi.org/10.21236/ada387245.

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Billups, Stephen C., and Layne T. Watson. A Probability-One Homotopy Algorithm for Nonsmooth Equations and Mixed Complementarity Problems. Defense Technical Information Center, 2000. http://dx.doi.org/10.21236/ada445723.

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Watson, Layne T. Theory and Application of Homotopy Techniques in Nonlinear Programming and Control Systems. Defense Technical Information Center, 1995. http://dx.doi.org/10.21236/ada294934.

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Hao, Wenrui, Jonathan D. Hauenstein, Chi-Wang Shu, Andrew J. Sommese, Zhiliang Xu, and Yong-Tao Zhang. A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws. Defense Technical Information Center, 2012. http://dx.doi.org/10.21236/ada568170.

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