Equivalences Of Classifying Spaces Completed At The Prime Two

Author : Robert Oliver
Publisher : American Mathematical Society(RI)
ISBN 13 : 9781470404529
Total Pages : 102 pages
Book Rating : 4.24/5 ( download)

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Download or read book Equivalences of Classifying Spaces Completed at the Prime Two written by Robert Oliver and published by American Mathematical Society(RI). This book was released on 2014-09-11 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction Higher limits over orbit categories Reduction to simple groups A relative version of $\Lambda$-functors Subgroups which contribute to higher limits Alternating groups Groups of Lie type in characteristic two Classical groups of Lie type in odd characteristic Exceptional groups of Lie type in odd characteristic Sproadic groups Computations of $\textrm{lim}^1(\mathcal{Z}_G)$ Bibliography

Author : Robert Oliver
Publisher : American Mathematical Soc.
ISBN 13 : 0821838288
Total Pages : 116 pages
Book Rating : 4.80/5 ( download)

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Download or read book Equivalences of Classifying Spaces Completed at the Prime Two written by Robert Oliver and published by American Mathematical Soc.. This book was released on 2006 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: We prove here the Martino-Priddy conjecture at the prime $2$: the $2$-completions of the classifying spaces of two finite groups $G$ and $G'$ are homotopy equivalent if and only if there is an isomorphism between their Sylow $2$-subgroups which preserves fusion. This is a consequence of a technical algebraic result, which says that for a finite group $G$, the second higher derived functor of the inverse limit vanishes for a certain functor $\mathcal{Z}_G$ on the $2$-subgroup orbit category of $G$. The proof of this result uses the classification theorem for finite simple groups.

Author : Bob Oliver
Publisher :
ISBN 13 :
Total Pages : 72 pages
Book Rating : 4.02/5 ( download)

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Download or read book Equivalences of Classifying Spaces Completed at the Prime Two written by Bob Oliver and published by . This book was released on 2003 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Katsuhiko Kuribayashi
Publisher : American Mathematical Soc.
ISBN 13 : 0821838563
Total Pages : 98 pages
Book Rating : 4.63/5 ( download)

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Download or read book Twisted Tensor Products Related to the Cohomology of the Classifying Spaces of Loop Groups written by Katsuhiko Kuribayashi and published by American Mathematical Soc.. This book was released on 2006 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $G$ be a compact, simply connected, simple Lie group. By applying the notion of a twisted tensor product in the senses of Brown as well as of Hess, we construct an economical injective resolution to compute, as an algebra, the cotorsion product which is the $E_2$-term of the cobar type Eilenberg-Moore spectral sequence converging to the cohomology of classifying space of the loop group $LG$. As an application, the cohomology $H^*(BLSpin(10); \mathbb{Z}/2)$ is explicitly determined as an $H^*(BSpin(10); \mathbb{Z}/2)$-module by using effectively the cobar type spectral sequence and the Hochschild spectral sequence, and further, by analyzing the TV-model for $BSpin(10)$.

Author : Paul Gregory Goerss
Publisher : American Mathematical Soc.
ISBN 13 : 0821832859
Total Pages : 520 pages
Book Rating : 4.51/5 ( download)

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Download or read book Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic $K$-Theory written by Paul Gregory Goerss and published by American Mathematical Soc.. This book was released on 2004 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: As part of its series of Emphasis Years in Mathematics, Northwestern University hosted an International Conference on Algebraic Topology. The purpose of the conference was to develop new connections between homotopy theory and other areas of mathematics. This proceedings volume grew out of that event. Topics discussed include algebraic geometry, cohomology of groups, algebraic $K$-theory, and $\mathbb{A 1$ homotopy theory. Among the contributors to the volume were Alejandro Adem,Ralph L. Cohen, Jean-Louis Loday, and many others. The book is suitable for graduate students and research mathematicians interested in homotopy theory and its relationship to other areas of mathematics.

Author : Michael Aschbacher
Publisher : Cambridge University Press
ISBN 13 : 1107601002
Total Pages : 329 pages
Book Rating : 4.00/5 ( download)

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Download or read book Fusion Systems in Algebra and Topology written by Michael Aschbacher and published by Cambridge University Press. This book was released on 2011-08-25 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. This book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians.

Author : Haynes Miller
Publisher : CRC Press
ISBN 13 : 1351251619
Total Pages : 982 pages
Book Rating : 4.17/5 ( download)

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Download or read book Handbook of Homotopy Theory written by Haynes Miller and published by CRC Press. This book was released on 2020-01-23 with total page 982 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.

Author : Tao Mei
Publisher : American Mathematical Soc.
ISBN 13 : 0821839802
Total Pages : 78 pages
Book Rating : 4.05/5 ( download)

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Download or read book Operator Valued Hardy Spaces written by Tao Mei and published by American Mathematical Soc.. This book was released on 2007 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author gives a systematic study of the Hardy spaces of functions with values in the noncommutative $Lp$-spaces associated with a semifinite von Neumann algebra $\mathcal{M .$ This is motivated by matrix valued Harmonic Analysis (operator weighted norm inequalities, operator Hilbert transform), as well as by the recent development of noncommutative martingale inequalities. in this paper noncommutative Hardy spaces are defined by noncommutative Lusin integral function, and it isproved that they are equivalent to those defined by noncommutative Littlewood-Paley G-functions. The main results of this paper include: (i) The analogue in the author's setting of the classical Fefferman duality theorem between $\mathcal{H 1$ and $\mathrm{BMO $. (ii) The atomic decomposition of theauthor's noncommutative $\mathcal{H 1.$ (iii) The equivalence between the norms of the noncommutative Hardy spaces and of the noncommutative $Lp$-spaces $(1

Author : Lars Inge Hedberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821839837
Total Pages : 112 pages
Book Rating : 4.36/5 ( download)

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Download or read book An Axiomatic Approach to Function Spaces, Spectral Synthesis, and Luzin Approximation written by Lars Inge Hedberg and published by American Mathematical Soc.. This book was released on 2007 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors define axiomatically a large class of function (or distribution) spaces on $N$-dimensional Euclidean space. The crucial property postulated is the validity of a vector-valued maximal inequality of Fefferman-Stein type. The scales of Besov spaces ($B$-spaces) and Lizorkin-Triebel spaces ($F$-spaces), and as a consequence also Sobolev spaces, and Bessel potential spaces, are included as special cases. The main results of Chapter 1 characterize our spaces by means of local approximations, higher differences, and atomic representations. In Chapters 2 and 3 these results are applied to prove pointwise differentiability outside exceptional sets of zero capacity, an approximation property known as spectral synthesis, a generalization of Whitney's ideal theorem, and approximation theorems of Luzin (Lusin) type.

Author : Jie Wu
Publisher : American Mathematical Soc.
ISBN 13 : 082183875X
Total Pages : 78 pages
Book Rating : 4.54/5 ( download)

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Download or read book On Maps from Loop Suspensions to Loop Spaces and the Shuffle Relations on the Cohen Groups written by Jie Wu and published by American Mathematical Soc.. This book was released on 2006 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: The maps from loop suspensions to loop spaces are investigated using group representations in this article. The shuffle relations on the Cohen groups are given. By using these relations, a universal ring for functorial self maps of double loop spaces of double suspensions is given. Moreover the obstructions to the classical exponent problem in homotopy theory are displayed in the extension groups of the dual of the important symmetric group modules Lie$(n)$, as well as in the top cohomology of the Artin braid groups with coefficients in the top homology of the Artin pure braid groups.