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Relevant bibliographies by topics / Adams spectral sequences. Homotopy groups

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Academic literature on the topic 'Adams spectral sequences. Homotopy groups'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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Journal articles on the topic "Adams spectral sequences. Homotopy groups"

1

Kato, Ryo, and Katsumi Shimomura. "The first line of the Bockstein spectral sequence on a monochromatic spectrum at an odd prime." Nagoya Mathematical Journal 207 (September 2012): 139–57. http://dx.doi.org/10.1017/s0027763000022339.

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AbstractThe chromatic spectral sequence was introduced by Miller, Ravenel, and Wilson to compute the E2-term of the Adams-Novikov spectral sequence for computing the stable homotopy groups of spheres. The E1-term of the spectral sequence is an Ext group of BP*BP-comodules. There is a sequence of Ext groups for nonnegative integers n with and there are Bockstein spectral sequences computing a module (n – s) from So far, a small number of the E1-terms are determined. Here, we determine the for p > 2 and n > 3 by computing the Bockstein spectral sequence with E1-term for s = 1, 2. As an app

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2

Baues, Hans-Joachim, and Mamuka Jibladze. "Dualization of the Hopf algebra of secondary cohomology operations and the Adams spectral sequence." Journal of K-Theory 7, no. 2 (2011): 203–347. http://dx.doi.org/10.1017/is010010029jkt133.

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AbstractWe describe the dualization of the algebra of secondary cohomology operations in terms of generators extending the Milnor dual of the Steenrod algebra. In this way we obtain explicit formulæ for the computation of the E3-term of the Adams spectral sequence converging to the stable homotopy groups of spheres.

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3

Smirnov, V. A. "Bott’s periodicity theorem and differentials of the Adams spectral sequence of homotopy groups of spheres." Mathematical Notes 84, no. 5-6 (2008): 710–17. http://dx.doi.org/10.1134/s0001434608110126.

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4

Bendersky, Martin, and John R. Hunton. "ON THE COALGEBRAIC RING AND BOUSFIELD–KAN SPECTRAL SEQUENCE FOR A LANDWEBER EXACT SPECTRUM." Proceedings of the Edinburgh Mathematical Society 47, no. 3 (2004): 513–32. http://dx.doi.org/10.1017/s0013091503000518.

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AbstractWe construct a Bousfield–Kan (unstable Adams) spectral sequence based on an arbitrary (and not necessarily connective) ring spectrum $E$ with unit and which is related to the homotopy groups of a certain unstable $E$ completion $X_E^{\wedge}$ of a space $X$. For $E$ an $\mathbb{S}$-algebra this completion agrees with that of the first author and Thompson. We also establish in detail the Hopf algebra structure of the unstable cooperations (the coalgebraic module) $E_*(\underline{E}_*)$ for an arbitrary Landweber exact spectrum $E$, extending work of the second author with Hopkins and wi

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5

Hu, Po, Igor Kriz, and Kyle Ormsby. "Remarks on motivic homotopy theory over algebraically closed fields." Journal of K-Theory 7, no. 1 (2010): 55–89. http://dx.doi.org/10.1017/is010001012jkt098.

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AbstractWe discuss certain calculations in the 2-complete motivic stable homotopy category over an algebraically closed field of characteristic 0. Specifically, we prove the convergence of motivic analogues of the Adams and Adams-Novikov spectral sequences, and as one application, discuss the 2-complete version of the complex motivic J -homomorphism.

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6

Ray, Nigel. "BORDISM, STABLE HOMOTOPY AND ADAMS SPECTRAL SEQUENCES (Fields Institute Monographs 7)." Bulletin of the London Mathematical Society 30, no. 1 (1998): 109–11. http://dx.doi.org/10.1112/s0024609397263459.

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7

Isaksen, Daniel C., Guozhen Wang, and Zhouli Xu. "Stable homotopy groups of spheres." Proceedings of the National Academy of Sciences 117, no. 40 (2020): 24757–63. http://dx.doi.org/10.1073/pnas.2012335117.

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We discuss the current state of knowledge of stable homotopy groups of spheres. We describe a computational method using motivic homotopy theory, viewed as a deformation of classical homotopy theory. This yields a streamlined computation of the first 61 stable homotopy groups and gives information about the stable homotopy groups in dimensions 62 through 90. As an application, we determine the groups of homotopy spheres that classify smooth structures on spheres through dimension 90, except for dimension 4. The method relies more heavily on machine computations than previous methods and is the

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8

Greenlees, J. P. C. "Homotopy equivariance, strict equivariance and induction theory." Proceedings of the Edinburgh Mathematical Society 35, no. 3 (1992): 473–92. http://dx.doi.org/10.1017/s0013091500005757.

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An obvious question occurs at the very start of equivariant homotopy theory. What is the relationship between maps equivariant up to homotopy and strictly equivariant maps? This question has been studied by various people, usually away from the group order ([8, 11, 22, 25, 26]). We consider the problem stably and answer it by giving a spectral sequence proceeding from homotopy equivariant to strictly equivariant information. The form of the spectral sequence is not surprising, but there are three distinctive features of our approach: (1) we show that the spectral sequence may be viewed as an A

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9

Lin, Wen-Hsiung. "Some infinite families in the stable homotopy of spheres." Mathematical Proceedings of the Cambridge Philosophical Society 101, no. 3 (1987): 477–85. http://dx.doi.org/10.1017/s0305004100066858.

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10

Díaz, Antonio, Albert Ruiz, and Antonio Viruel. "Cohomological uniqueness of some p-groups." Proceedings of the Edinburgh Mathematical Society 56, no. 2 (2012): 449–68. http://dx.doi.org/10.1017/s0013091512000247.

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AbstractWe consider classifying spaces of a family of p-groups and prove that mod p cohomology enriched with Bockstein spectral sequences determines their homotopy type among p-completed CW-complexes.

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Dissertations / Theses on the topic "Adams spectral sequences. Homotopy groups"

1

Nave, Lee Stewart. "The cohomology of finite subgroups of Morava stabilizer groups and Smith-Toda complexes /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/5803.

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2

Zapata, Cesar Augusto Ipanaque. "Espaços de configurações." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-12072017-164714/.

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O objetivo principal deste trabalho será apresentar um estudo detalhado dos espaços de configurações. Dissertaremos sobre: espaços de configurações clássicos, invariância do bordo, espaço de configurações para superfícies, fibração de Fadell e Neuwirth e espaços de configurações do espaço Euclideano, da esfera e do espaço projetivo complexo.<br>The main objective of this work will be to present a detailed study of the configuration spaces. We will study: classical configuration spaces, invariance of the boundary, configuration spaces of surfaces, Fadell and Neuwirth fibration and configuration

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3

Behrens, Mark. "Root invariants in the Adams spectral sequence /." 2003. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:3088714.

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Books on the topic "Adams spectral sequences. Homotopy groups"

1

Computing the homology of the lambda algebra. American Mathematical Society, 1985.

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2

Kochman, Stanley O. Bordism, stable homotopy, and Adams spectral sequences. American Mathematical Society, 1996.

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3

Complex cobordism and stable homotopy groups of spheres. 2nd ed. AMS Chelsea Pub., 2004.

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4

Complex cobordism and stable homotopy groups of spheres. Academic Press, 1986.

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5

The Goodwillie tower and the EHP sequence. American Mathematical Society, 2012.

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Vb1s-periodic Homotopy Groups Of So(n (Memoirs of the American Mathematical Society). American Mathematical Society, 2004.

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Book chapters on the topic "Adams spectral sequences. Homotopy groups"

1

"The classical Adams spectral sequence." In Complex Cobordism and Stable Homotopy Groups of Spheres. American Mathematical Society, 2003. http://dx.doi.org/10.1090/chel/347/03.

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2

"The homotopy groups of 𝑡𝑚𝑓." In The Adams Spectral Sequence for Topological Modular Forms. American Mathematical Society, 2021. http://dx.doi.org/10.1090/surv/253/10.

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3

"Setting up the Adams spectral sequence." In Complex Cobordism and Stable Homotopy Groups of Spheres. American Mathematical Society, 2003. http://dx.doi.org/10.1090/chel/347/02.

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4

"𝐵𝑃-theory and the Adams-Novikov spectral sequence." In Complex Cobordism and Stable Homotopy Groups of Spheres. American Mathematical Society, 2003. http://dx.doi.org/10.1090/chel/347/04.

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5

"Computing stable homotopy groups with the Adams-Novikov spectral sequence." In Complex Cobordism and Stable Homotopy Groups of Spheres. American Mathematical Society, 2003. http://dx.doi.org/10.1090/chel/347/07.

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6

"Chapter 7 Computing Stable Homotopy Groups with the Adams-Novikov Spectral Sequence." In Pure and Applied Mathematics. Elsevier, 1986. http://dx.doi.org/10.1016/s0079-8169(08)61010-7.

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7

"Bordism." In Bordism, Stable Homotopy and Adams Spectral Sequences. American Mathematical Society, 1996. http://dx.doi.org/10.1090/fim/007/01.

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8

"Characteristic classes." In Bordism, Stable Homotopy and Adams Spectral Sequences. American Mathematical Society, 1996. http://dx.doi.org/10.1090/fim/007/02.

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9

"Stable category." In Bordism, Stable Homotopy and Adams Spectral Sequences. American Mathematical Society, 1996. http://dx.doi.org/10.1090/fim/007/03.

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"Complex bordism." In Bordism, Stable Homotopy and Adams Spectral Sequences. American Mathematical Society, 1996. http://dx.doi.org/10.1090/fim/007/04.

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