Proper Equivariant Stable Homotopy Theory
Author: Dieter Degrijse
Publisher: American Mathematical Society
Published: 2023-09-15
Total Pages: 154
ISBN-13: 1470467046
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Equivariant Stable Homotopy Theory
Author: L. Gaunce Jr. Lewis
Publisher: Springer
Published: 2006-11-14
Total Pages: 548
ISBN-13: 3540470778
DOWNLOAD EBOOKThis 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
Author: Stefan Schwede
Publisher: Cambridge University Press
Published: 2018-09-06
Total Pages: 847
ISBN-13: 110842581X
DOWNLOAD EBOOKA 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
Author: Michael A. Hill
Publisher: Cambridge University Press
Published: 2021-07-29
Total Pages: 881
ISBN-13: 1108831443
DOWNLOAD EBOOKA complete and definitive account of the authors' resolution of the Kervaire invariant problem in stable homotopy theory.
Equivariant Homotopy and Cohomology Theory
Author: J. Peter May
Publisher: American Mathematical Soc.
Published: 1996
Total Pages: 384
ISBN-13: 0821803190
DOWNLOAD EBOOKThis 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.
Equivariant Stable Homotopy Theory
Author: L. Gaunce Jr. Lewis
Publisher:
Published: 2014-01-15
Total Pages: 552
ISBN-13: 9783662170328
DOWNLOAD EBOOKAxiomatic Stable Homotopy Theory
Author: Mark Hovey
Publisher: American Mathematical Soc.
Published: 1997
Total Pages: 130
ISBN-13: 0821806246
DOWNLOAD EBOOKWe define and investigate a class of categories with formal properties similar to those of the homotopy category of spectra. This class includes suitable versions of the derived category of modules over a commutative ring, or of comodules over a commutative Hopf algebra, and is closed under Bousfield localization. We study various notions of smallness, questions about representability of (co)homology functors, and various kinds of localization. We prove theorems analogous to those of Hopkins and Smith about detection of nilpotence and classification of thick subcategories. We define the class of Noetherian stable homotopy categories, and investigate their special properties. Finally, we prove that a number of categories occurring in nature (including those mentioned above) satisfy our axioms.
Rational $S^1$-Equivariant Stable Homotopy Theory
Author: John Patrick Campbell Greenlees
Publisher: American Mathematical Soc.
Published: 1999
Total Pages: 306
ISBN-13: 0821810014
DOWNLOAD EBOOKThe 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.
Nilpotence and Periodicity in Stable Homotopy Theory
Author: Douglas C. Ravenel
Publisher: Princeton University Press
Published: 1992-11-08
Total Pages: 228
ISBN-13: 9780691025728
DOWNLOAD EBOOKNilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.
Global Homotopy Theory
Author: Stefan Schwede
Publisher: Cambridge University Press
Published: 2018-09-06
Total Pages: 848
ISBN-13: 1108593658
DOWNLOAD EBOOKEquivariant homotopy theory started from geometrically motivated questions about symmetries of manifolds. Several important equivariant phenomena occur not just for a particular group, but in a uniform way for all groups. Prominent examples include stable homotopy, K-theory or bordism. Global equivariant homotopy theory studies such uniform phenomena, i.e. universal symmetries encoded by simultaneous and compatible actions of all compact Lie groups. This book introduces graduate students and researchers to global equivariant homotopy theory. The framework is based on the new notion of global equivalences for orthogonal spectra, a much finer notion of equivalence than is traditionally considered. The treatment is largely self-contained and contains many examples, making it suitable as a textbook for an advanced graduate class. At the same time, the book is a comprehensive research monograph with detailed calculations that reveal the intrinsic beauty of global equivariant phenomena.
