Twisted Tensor Products Related To The Cohomology Of The Classifying Spaces Of Loop Groups

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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 Mathematics 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 $BSpin(10)$.

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 Society(RI)
Release Date : 2014-09-11

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 Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Cohomology operations categories.

Introduction The mod 2 cohomology of $BLSO(n)$ The mod 2 cohomology of $BLG$ for $G=Spin(n)\ (7\leq n\leq 9)$ The mod 2 cohomology of $BLG$ for $G=G_2,F_4$ A multiplication on a twisted tensor product The twisted tensor product associated with $H^*(Spin(N);\mathbb{Z}/2)$ A manner for calculating the homology of a DGA The Hochschild spectral sequence Proof of Theorem 1.6 Computation of a cotorsion product of $H^*(Spin(10);\mathbb{Z}/2)$ and the Hochschild homology of $H^*(BSpin(10);\mathbb{Z}/2)$ Proof of Theorem 1.7 Proofs of Proposition 1.9 and Theorem 1.10 Appendix Bibliography

Equivalences Of Classifying Spaces Completed At The Prime Two

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Author : Robert Oliver
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Equivalences Of Classifying Spaces Completed At The Prime Two written by Robert 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 Mathematics 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.

Steenrod Squares In Spectral Sequences

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Author : William M. Singer
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Steenrod Squares In Spectral Sequences written by William M. Singer 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 Mathematics categories.

This book develops a general theory of Steenrod operations in spectral sequences. It gives special attention to the change-of-rings spectral sequence for the cohomology of an extension of Hopf algebras and to the Eilenberg-Moore spectral sequence for the cohomology of classifying spaces and homotopy orbit spaces. In treating the change-of-rings spectral sequence, the book develops from scratch the necessary properties of extensions of Hopf algebras and constructs the spectral sequence in a form particularly suited to the introduction of Steenrod squares. The resulting theory can be used effectively for the computation of the cohomology rings of groups and Hopf algebras, and of the Steenrod algebra in particular, and so should play a useful role in stable homotopy theory. Similarly the book offers a self-contained construction of the Eilenberg-Moore spectral sequence, in a form suitable for the introduction of Steenrod operations. The corresponding theory is an effective tool for the computation of t

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 Mathematics 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.

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 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

Betti Numbers Of The Moduli Space Of Rank 3 Parabolic Higgs Bundles

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Author : Oscar García-Prada
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

Betti Numbers Of The Moduli Space Of Rank 3 Parabolic Higgs Bundles written by Oscar García-Prada 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.

Parabolic Higgs bundles on a Riemann surface are of interest for many reasons, one of them being their importance in the study of representations of the fundamental group of the punctured surface in the complex general linear group. in this paper the authors calculate the Betti numbers of the moduli space of rank 3 parabolic Higgs bundles with fixed and non-fixed determinant, using Morse theory. A key point is that certain critical submanifolds of the Morse function can be identified with moduli spaces of parabolic triples. These moduli spaces come in families depending on a real parameter and the authors carry out a careful analysis of them by studying their variation with this parameter. Thus the authors obtain in particular information about the topology of the moduli spaces of parabolic triples for the value of the parameter relevant to the study of parabolic Higgs bundles. The remaining critical submanifolds are also described: one of them is the moduli space of parabolic bundles, while the rem

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 Necessary And Sufficient Conditions For L P Estimates Of Riesz Transforms Associated To Elliptic Operators On Mathbb R N And Related Estimates

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Author : Pascal Auscher
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

On Necessary And Sufficient Conditions For L P Estimates Of Riesz Transforms Associated To Elliptic Operators On Mathbb R N And Related Estimates written by Pascal Auscher 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.

This memoir focuses on $Lp$ estimates for objects associated to elliptic operators in divergence form: its semigroup, the gradient of the semigroup, functional calculus, square functions and Riesz transforms. The author introduces four critical numbers associated to the semigroup and its gradient that completely rule the ranges of exponents for the $Lp$ estimates. It appears that the case $p2$ which is new. The author thus recovers in a unified and coherent way many $Lp$ estimates and gives further applications. The key tools from harmonic analysis are two criteria for $Lp$ boundedness, one for $p2$ but in ranges different from the usual intervals $(1,2)$ and $(2,\infty)$.

Symmetric And Alternating Groups As Monodromy Groups Of Riemann Surfaces I Generic Covers And Covers With Many Branch Points

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Author : Robert M. Guralnick
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

Symmetric And Alternating Groups As Monodromy Groups Of Riemann Surfaces I Generic Covers And Covers With Many Branch Points written by Robert M. Guralnick 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.

Considers indecomposable degree $n$ covers of Riemann surfaces with monodromy group an alternating or symmetric group of degree $d$. The authors show that if the cover has five or more branch points then the genus grows rapidly with $n$ unless either $d = n$ or the curves have genus zero, there are precisely five branch points and $n =d(d-1)/2$.