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Equivariant Stable Homotopy Theory

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 778/5 ( reviews)

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Book Synopsis Equivariant Stable Homotopy Theory by : L. Gaunce Jr. Lewis

Download or read book Equivariant Stable Homotopy Theory written by L. Gaunce Jr. Lewis. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem

2021-07-29 Mathematics
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Release : 2021-07-29
Genre : Mathematics
Kind : eBook
Book Rating : 443/5 ( reviews)

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Book Synopsis Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem by : Michael A. Hill

Download or read book Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem written by Michael A. Hill. This book was released on 2021-07-29. Available in PDF, EPUB and Kindle. Book excerpt: A complete and definitive account of the authors' resolution of the Kervaire invariant problem in stable homotopy theory.

Equivariant Homotopy and Cohomology Theory

1996 Mathematics
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Release : 1996
Genre : Mathematics
Kind : eBook
Book Rating : 190/5 ( reviews)

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Book Synopsis Equivariant Homotopy and Cohomology Theory by : J. Peter May

Download or read book Equivariant Homotopy and Cohomology Theory written by J. Peter May. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Global Homotopy Theory

2018-09-06 Mathematics
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Release : 2018-09-06
Genre : Mathematics
Kind : eBook
Book Rating : 81X/5 ( reviews)

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Book Synopsis Global Homotopy Theory by : Stefan Schwede

Download or read book Global Homotopy Theory written by Stefan Schwede. This book was released on 2018-09-06. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, self-contained approach to global equivariant homotopy theory, with many detailed examples and sample calculations.

Topics in Equivariant Stable Homotopy Theory

2011
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Release : 2011
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Kind : eBook
Book Rating : 333/5 ( reviews)

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Book Synopsis Topics in Equivariant Stable Homotopy Theory by : Anna Marie Riehle Bohmann

Download or read book Topics in Equivariant Stable Homotopy Theory written by Anna Marie Riehle Bohmann. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: Finally, we give an alternate description of the multiplicative norm maps used in recent work on the Kervaire invariant one problem. Comparing our construction with that used in [17] gives insight into the mechanism of norm maps.

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