Equivalences Of Classifying Spaces Completed At The Prime Two
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Equivalences Of Classifying Spaces Completed At The Prime Two
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Author : Bob Oliver
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Equivalences Of Classifying Spaces Completed At The Prime Two written by Bob Oliver and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Classifying spaces categories.
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.
Twisted Tensor Products Related To The Cohomology Of The Classifying Spaces Of Loop Groups
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Author : Katsuhiko Kuribayashi
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Twisted Tensor Products Related To The Cohomology Of The Classifying Spaces Of Loop Groups written by Katsuhiko Kuribayashi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Cohomology operations categories.
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 $BSpin(10)$.
Homotopy Theory Relations With Algebraic Geometry Group Cohomology And Algebraic K Theory
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Author : Paul Gregory Goerss
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Homotopy Theory Relations With Algebraic Geometry Group Cohomology And Algebraic K Theory written by Paul Gregory Goerss and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.
Classifying Spaces And Fibrations
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Author : J. Peter May
language : en
Publisher: American Mathematical Soc.
Release Date : 1975
Classifying Spaces And Fibrations written by J. Peter May and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Classifying spaces categories.
The basic theory of fibrations is generalized to a context in which fibres, and maps on fibres, are constrained to lie in any preassigned category of spaces [script capital] F. Then axioms are placed on [script capital] F to allow the development of a theory of associated principal fibrations and, under several choices of additional hypotheses on [script capital] F, a classification theorem is proven for such fibrations.
Fusion Systems In Algebra And Topology
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Author : Michael Aschbacher
language : en
Publisher: Cambridge University Press
Release Date : 2011-08-25
Fusion Systems In Algebra And Topology written by Michael Aschbacher and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-25 with Mathematics categories.
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.
Handbook Of Homotopy Theory
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Author : Haynes Miller
language : en
Publisher: CRC Press
Release Date : 2020-01-23
Handbook Of Homotopy Theory written by Haynes Miller and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-23 with Mathematics categories.
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.
Classifying Spaces Of Sporadic Groups
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Author : David J. Benson
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Classifying Spaces Of Sporadic Groups written by David J. Benson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
For each of the 26 sporadic finite simple groups, the authors construct a 2-completed classifying space using a homotopy decomposition in terms of classifying spaces of suitable 2-local subgroups. This construction leads to an additive decomposition of the mod 2 group cohomology.
Operator Valued Hardy Spaces
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Author : Tao Mei
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Operator Valued Hardy Spaces written by Tao Mei and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
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 is proved 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 the author's noncommutative $\mathcal{H 1.$ (iii) The equivalence between the norms of the noncommutative Hardy spaces and of the noncommutative $Lp$-spaces $(1 \infty )$. (iv) The noncommutative Hardy-Littlewood maximal inequality. (v) A description of BMO as an intersection of two dyadic BMO. (vi) The interpolation results on these Hardy spaces.
An Axiomatic Approach To Function Spaces Spectral Synthesis And Luzin Approximation
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Author : Lars Inge Hedberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
An Axiomatic Approach To Function Spaces Spectral Synthesis And Luzin Approximation written by Lars Inge Hedberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
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.
On Maps From Loop Suspensions To Loop Spaces And The Shuffle Relations On The Cohen Groups
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Author : Jie Wu
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
On Maps From Loop Suspensions To Loop Spaces And The Shuffle Relations On The Cohen Groups written by Jie Wu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Algebra, Homological categories.
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.