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Author : Kristian J. Moi
Publisher :
ISBN 13 :
Total Pages : 118 pages
Book Rating : 4.:/5 (913 download)
Download or read book Equivariant Homotopy Theory and K-theory of Exact Categories with Duality written by Kristian J. Moi and published by . This book was released on 2014 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kristian J. Moi
Publisher :
ISBN 13 : 9788770789707
Total Pages : pages
Book Rating : 4.7/5 (897 download)
Download or read book Equivariant Homotopy Theory and K-theory of Exact Categories with Duality written by Kristian J. Moi and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. Peter May
Publisher : American Mathematical Soc.
ISBN 13 : 0821803190
Total Pages : 384 pages
Book Rating : 4.8/5 (218 download)
Download or read book Equivariant Homotopy and Cohomology Theory written by J. Peter May and published by American Mathematical Soc.. This book was released on 1996 with total page 384 pages. 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.
Author : L. Gaunce Jr. Lewis
Publisher : Springer
ISBN 13 : 3540470778
Total Pages : 548 pages
Book Rating : 4.5/5 (44 download)
Download or read book Equivariant Stable Homotopy Theory written by L. Gaunce Jr. Lewis and published by Springer. This book was released on 2006-11-14 with total page 548 pages. 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.
Author : M. Cole
Publisher : American Mathematical Soc.
ISBN 13 : 0821889354
Total Pages : 384 pages
Book Rating : 4.8/5 (218 download)
Download or read book Equivariant Homotopy and Cohomology Theory written by M. Cole and published by American Mathematical Soc.. This book was released on 1996-01-01 with total page 384 pages. 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.
Author : Michael A. Hill
Publisher : Cambridge University Press
ISBN 13 : 1108831443
Total Pages : 881 pages
Book Rating : 4.1/5 (88 download)
Download or read book Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem written by Michael A. Hill and published by Cambridge University Press. This book was released on 2021-07-29 with total page 881 pages. 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.
Author : Eric Friedlander
Publisher : Springer Science & Business Media
ISBN 13 : 354023019X
Total Pages : 1148 pages
Book Rating : 4.5/5 (42 download)
Download or read book Handbook of K-Theory written by Eric Friedlander and published by Springer Science & Business Media. This book was released on 2005-07-18 with total page 1148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.
Author : Guillermo Cortiñas
Publisher : European Mathematical Society
ISBN 13 : 9783037190609
Total Pages : 460 pages
Book Rating : 4.1/5 (96 download)
Download or read book K-theory and Noncommutative Geometry written by Guillermo Cortiñas and published by European Mathematical Society. This book was released on 2008 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its inception 50 years ago, K-theory has been a tool for understanding a wide-ranging family of mathematical structures and their invariants: topological spaces, rings, algebraic varieties and operator algebras are the dominant examples. The invariants range from characteristic classes in cohomology, determinants of matrices, Chow groups of varieties, as well as traces and indices of elliptic operators. Thus K-theory is notable for its connections with other branches of mathematics. Noncommutative geometry develops tools which allow one to think of noncommutative algebras in the same footing as commutative ones: as algebras of functions on (noncommutative) spaces. The algebras in question come from problems in various areas of mathematics and mathematical physics; typical examples include algebras of pseudodifferential operators, group algebras, and other algebras arising from quantum field theory. To study noncommutative geometric problems one considers invariants of the relevant noncommutative algebras. These invariants include algebraic and topological K-theory, and also cyclic homology, discovered independently by Alain Connes and Boris Tsygan, which can be regarded both as a noncommutative version of de Rham cohomology and as an additive version of K-theory. There are primary and secondary Chern characters which pass from K-theory to cyclic homology. These characters are relevant both to noncommutative and commutative problems and have applications ranging from index theorems to the detection of singularities of commutative algebraic varieties. The contributions to this volume represent this range of connections between K-theory, noncommmutative geometry, and other branches of mathematics.
Author : Victor Percy Snaith
Publisher : American Mathematical Soc.
ISBN 13 : 0821822802
Total Pages : 117 pages
Book Rating : 4.8/5 (218 download)
Download or read book Algebraic $K$-Theory and Localised Stable Homotopy Theory written by Victor Percy Snaith and published by American Mathematical Soc.. This book was released on 1983 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is a homomorphism from the stable homotopy of the classifying space of the group of units in a ring to its algebraic [italic]K-theory. When the ring has enough roots of unity a "Bott element" exists in these groups (taken with coefficients). We compute the groups obtained by inverting the Bott element. This computation is used in conjunction with homomorphism to construct algebraic [italic]K-theory classes and to give upper bounds on [italic]K-theory with the Bott element inverted.
Author : Michael Charles Crabb
Publisher : Cambridge University Press
ISBN 13 : 0521280516
Total Pages : 137 pages
Book Rating : 4.5/5 (212 download)
Download or read book ZZ/2 - Homotopy Theory written by Michael Charles Crabb and published by Cambridge University Press. This book was released on 1980-11-28 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This account is a study of twofold symmetry in algebraic topology. The author discusses specifically the antipodal involution of a real vector bundle - multiplication by - I in each fibre; doubling and squaring operations; the symmetry of bilinear forms and Hermitian K-theory. In spite of its title, this is not a treatise on equivariant topology; rather it is the language in which to describe the symmetry. Familiarity with the basic concepts of algebraic topology (homotopy, stable homotopy, homology, K-theory, the Pontrjagin-Thom transfer construction) is assumed. Detailed proofs are not given (the expert reader will be able to supply them when necessary) yet nowhere is credibility lost. Thus the approach is elementary enough to provide an introduction to the subject suitable for graduate students although research workers will find here much of interest.
Author : Emily Riehl
Publisher : Cambridge University Press
ISBN 13 : 1139952633
Total Pages : 371 pages
Book Rating : 4.1/5 (399 download)
Download or read book Categorical Homotopy Theory written by Emily Riehl and published by Cambridge University Press. This book was released on 2014-05-26 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.
Author : Stefan Schwede
Publisher : Cambridge University Press
ISBN 13 : 1108593658
Total Pages : 848 pages
Book Rating : 4.1/5 (85 download)
Download or read book Global Homotopy Theory written by Stefan Schwede and published by Cambridge University Press. This book was released on 2018-09-06 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt: Equivariant 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.
Author : Robert Neil Vance
Publisher :
ISBN 13 :
Total Pages : 178 pages
Book Rating : 4.X/5 (1 download)
Download or read book Homotopy Equivariant Group Actions and Atiyah-real Algebraic K-theory written by Robert Neil Vance and published by . This book was released on 1974 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Douglas C. Ravenel
Publisher : Princeton University Press
ISBN 13 : 9780691025728
Total Pages : 228 pages
Book Rating : 4.0/5 (257 download)
Download or read book Nilpotence and Periodicity in Stable Homotopy Theory written by Douglas C. Ravenel and published by Princeton University Press. This book was released on 1992-11-08 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nilpotence 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.
Author : I. M. James
Publisher : Elsevier
ISBN 13 : 1483184765
Total Pages : 468 pages
Book Rating : 4.4/5 (831 download)
Download or read book Homotopy Theory written by I. M. James and published by Elsevier. This book was released on 2014-05-09 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homotopy Theory contains all the published mathematical work of J. H. C. Whitehead, written between 1947 and 1955. This volume considers the study of simple homotopy types, particularly the realization of problem for homotopy types. It describes Whitehead's version of homotopy theory in terms of CW-complexes. This book is composed of 21 chapters and begins with an overview of a theorem to Borsuk and the homotopy type of ANR. The subsequent chapters deal with four-dimensional polyhedral, the homotopy type of a special kind of polyhedron, and the combinatorial homotopy I and II. These topics are followed by reviews of other homotopy types, such as group extensions with homotopy operators, cohomology systems, secondary boundary operator, algebraic homotopy, and the G-dual of a semi-exact couple. The last chapters examine the connected complex homotopy types and the second non-vanishing homotopy groups. This book will be of great value to mathematicians.
Author : Peter Hilton
Publisher : Taylor & Francis Group
ISBN 13 :
Total Pages : 246 pages
Book Rating : 4.3/5 (91 download)
Download or read book Homotopy Theory and Duality written by Peter Hilton and published by Taylor & Francis Group. This book was released on 1966 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gonçalo Tabuada
Publisher : American Mathematical Soc.
ISBN 13 : 1470423979
Total Pages : 127 pages
Book Rating : 4.4/5 (74 download)
Download or read book Noncommutative Motives written by Gonçalo Tabuada and published by American Mathematical Soc.. This book was released on 2015-09-21 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of motives began in the early 1960s when Grothendieck envisioned the existence of a "universal cohomology theory of algebraic varieties". The theory of noncommutative motives is more recent. It began in the 1980s when the Moscow school (Beilinson, Bondal, Kapranov, Manin, and others) began the study of algebraic varieties via their derived categories of coherent sheaves, and continued in the 2000s when Kontsevich conjectured the existence of a "universal invariant of noncommutative algebraic varieties". This book, prefaced by Yuri I. Manin, gives a rigorous overview of some of the main advances in the theory of noncommutative motives. It is divided into three main parts. The first part, which is of independent interest, is devoted to the study of DG categories from a homotopical viewpoint. The second part, written with an emphasis on examples and applications, covers the theory of noncommutative pure motives, noncommutative standard conjectures, noncommutative motivic Galois groups, and also the relations between these notions and their commutative counterparts. The last part is devoted to the theory of noncommutative mixed motives. The rigorous formalization of this latter theory requires the language of Grothendieck derivators, which, for the reader's convenience, is revised in a brief appendix.
