Rational $S^1$-Equivariant Stable Homotopy Theory

Rational $S^1$-Equivariant Stable Homotopy Theory PDF Author: John Patrick Campbell Greenlees
Publisher: American Mathematical Soc.
ISBN: 0821810014
Category : Mathematics
Languages : en
Pages : 306

Get Book Here

Book Description
The memoir presents a systematic study of rational S1-equivariant cohomology theories, and a complete algebraic model for them. It provides a classification of such cohomology theories in simple algebraic terms and a practical means of calculation. The power of the model is illustrated by analysis of the Segal conjecture, the behaviour of the Atiyah-Hirzebruch spectral sequence, the structure of S1-equivariant K-theory, and the rational behaviour of cyclotomic spectra and the topological cyclic homology construction.

Rational $S^1$-Equivariant Stable Homotopy Theory

Rational $S^1$-Equivariant Stable Homotopy Theory PDF Author: John Patrick Campbell Greenlees
Publisher: American Mathematical Soc.
ISBN: 0821810014
Category : Mathematics
Languages : en
Pages : 306

Get Book Here

Book Description
The memoir presents a systematic study of rational S1-equivariant cohomology theories, and a complete algebraic model for them. It provides a classification of such cohomology theories in simple algebraic terms and a practical means of calculation. The power of the model is illustrated by analysis of the Segal conjecture, the behaviour of the Atiyah-Hirzebruch spectral sequence, the structure of S1-equivariant K-theory, and the rational behaviour of cyclotomic spectra and the topological cyclic homology construction.

Rational S-Equivariant Stable Homotopy Theory

Rational S-Equivariant Stable Homotopy Theory PDF Author: John Patrick Campbell Greenlees
Publisher: American Mathematical Society(RI)
ISBN: 9781470402501
Category : MATHEMATICS
Languages : en
Pages : 306

Get Book Here

Book Description
A systematic study of rational S1-equivariant cohomology theories and a complete algebraic model for them. It provides a classification of such cohomology theories in simple algebraic terms and a practical means of calculation. The power of the model is illustrated by analysis of the Segal conjecture, the behaviour of the Atiyah-Hirzebruch spectral sequence, the structure of S1-equivariant K-theory, and the rational behaviour of cyclotomic spectra and the topological cyclic homology construction.

Equivariant Homotopy and Cohomology Theory

Equivariant Homotopy and Cohomology Theory PDF Author: J. Peter May
Publisher: American Mathematical Soc.
ISBN: 0821803190
Category : Mathematics
Languages : en
Pages : 384

Get Book Here

Book Description
This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The works begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. The book then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology. Finally, the book gives an introduction to "brave new algebra", the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail.

Rational S1-equivariant Stable Homotopy Theory

Rational S1-equivariant Stable Homotopy Theory PDF Author:
Publisher: American Mathematical Soc.
ISBN: 9780821863848
Category : Mathematics
Languages : en
Pages : 308

Get Book Here

Book Description
The memoir presents a systematic study of rational $S^1$-equivariant cohomology theories, and a complete algebraic model for them. It provides a classification of such cohomology theories in simple algebraic terms and a practical means of calculation. The power of the model is illustrated by analysis of the Segal conjecture, the behaviour of the Atiyah-Hirzebruch spectral sequence, the structure of $S^1$-equivariant $K$-theory, and the rational behaviour of cyclotomic spectra and the topological cyclic homology construction.

Equivariant Stable Homotopy Theory

Equivariant Stable Homotopy Theory PDF Author: L. Gaunce Jr. Lewis
Publisher: Springer
ISBN: 3540470778
Category : Mathematics
Languages : en
Pages : 548

Get Book Here

Book Description
This book is a foundational piece of work in stable homotopy theory and in the theory of transformation groups. It may be roughly divided into two parts. The first part deals with foundations of (equivariant) stable homotopy theory. A workable category of CW-spectra is developed. The foundations are such that an action of a compact Lie group is considered throughout, and spectra allow desuspension by arbitrary representations. But even if the reader forgets about group actions, he will find many details of the theory worked out for the first time. More subtle constructions like smash products, function spectra, change of group isomorphisms, fixed point and orbit spectra are treated. While it is impossible to survey properly the material which is covered in the book, it does boast these general features: (i) a thorough and reliable presentation of the foundations of the theory; (ii) a large number of basic results, principal applications, and fundamental techniques presented for the first time in a coherent theory, unifying numerous treatments of special cases in the literature.

Global Homotopy Theory

Global Homotopy Theory PDF Author: Stefan Schwede
Publisher: Cambridge University Press
ISBN: 110842581X
Category : Mathematics
Languages : en
Pages : 847

Get Book Here

Book Description
A comprehensive, self-contained approach to global equivariant homotopy theory, with many detailed examples and sample calculations.

Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem

Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem PDF Author: Michael A. Hill
Publisher: Cambridge University Press
ISBN: 1108831443
Category : Mathematics
Languages : en
Pages : 881

Get Book Here

Book Description
A complete and definitive account of the authors' resolution of the Kervaire invariant problem in stable homotopy theory.

Asymptotics for Solutions of Linear Differential Equations Having Turning Points with Applications

Asymptotics for Solutions of Linear Differential Equations Having Turning Points with Applications PDF Author: Shlomo Strelitz
Publisher: American Mathematical Soc.
ISBN: 0821813528
Category : Mathematics
Languages : en
Pages : 105

Get Book Here

Book Description
Asymptotics are built for the solutions $y_j(x, \lambda)$, $y_j DEGREES{(k)}(0, \lambda)=\delta_{j\, n-k}$, $0\le j, k+1\le n$ of the equation $L(y)=\lambda p(x)y, \quad x\in [0,1], $ where $L(y)$ is a linear differential operator of whatever order $n\ge 2$ and $p(x)$ is assumed to possess a finite number of turning points. The established asymptotics are afterwards applied to the study of: 1) the existence of infinite eigenvalue sequences for various multipoint boundary problems posed on $L(y)=\lambda p(x)y, \quad x\in [0,1], $, especially as $n=2$ and $n=3$ (let us be aware that the same method can be successfully applied on many occasions in case $n>3$ too) and 2) asymptotical distribution of the corresponding eigenvalue sequences on the

A Computation of $\delta ^1_5$

A Computation of $\delta ^1_5$ PDF Author: Steve Jackson
Publisher: American Mathematical Soc.
ISBN: 082181091X
Category : Mathematics
Languages : en
Pages : 109

Get Book Here

Book Description
This book is intended for graduate students and research mathematicians working in logic and foundations

Norms on Possibilities. I: Forcing with Trees and Creatures

Norms on Possibilities. I: Forcing with Trees and Creatures PDF Author: Andrzej Rosłanowski
Publisher: American Mathematical Soc.
ISBN: 0821811800
Category : Gardening
Languages : en
Pages : 186

Get Book Here

Book Description
This book is intended for graduate students and research mathematicians interested in mathematical logic and foundations.