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Download or read book The Equivariant Stable Homotopy Theory Around Isometric Linear Maps written by and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : 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 : Dieter Degrijse
Publisher : American Mathematical Society
ISBN 13 : 1470467046
Total Pages : 154 pages
Book Rating : 4.4/5 (74 download)
Download or read book Proper Equivariant Stable Homotopy Theory written by Dieter Degrijse and published by American Mathematical Society. This book was released on 2023-09-15 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Author : Anthony D. Elmendorf
Publisher : American Mathematical Soc.
ISBN 13 : 0821843036
Total Pages : 265 pages
Book Rating : 4.8/5 (218 download)
Download or read book Rings, Modules, and Algebras in Stable Homotopy Theory written by Anthony D. Elmendorf and published by American Mathematical Soc.. This book was released on 1997 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a new point-set level approach to stable homotopy theory that has already had many applications and promises to have a lasting impact on the subject. Given the sphere spectrum $S$, the authors construct an associative, commutative, and unital smash product in a complete and cocomplete category of ``$S$-modules'' whose derived category is equivalent to the classical stable homotopy category. This construction allows for a simple and algebraically manageable definition of ``$S$-algebras'' and ``commutative $S$-algebras'' in terms of associative, or associative and commutative, products $R\wedge SR \longrightarrow R$. These notions are essentially equivalent to the earlier notions of $A {\infty $ and $E {\infty $ ring spectra, and the older notions feed naturally into the new framework to provide plentiful examples. There is an equally simple definition of $R$-modules in terms of maps $R\wedge SM\longrightarrow M$. When $R$ is commutative, the category of $R$-modules also has a
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 : William G. Dwyer
Publisher : American Mathematical Soc.
ISBN 13 : 9780821871263
Total Pages : 328 pages
Book Rating : 4.8/5 (712 download)
Download or read book Stable and Unstable Homotopy written by William G. Dwyer and published by American Mathematical Soc.. This book was released on 1998-01-01 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of workshops on stable homotopy theory and on unstable homotopy theory held at The Fields Institute as part of the homotopy program during the year 1996. The papers in the volume describe current research in the subject, and all included works were refereed. Rather than being a summary of work to be published elsewhere, each paper is the unique source for the new material it contains. The book contains current research from international experts in the subject area, and presents open problems with directions for future research.
Author : J.F. Adams
Publisher : Springer
ISBN 13 : 3662159058
Total Pages : 84 pages
Book Rating : 4.6/5 (621 download)
Download or read book Stable Homotopy Theory written by J.F. Adams and published by Springer. This book was released on 2013-11-11 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : L. Gaunce Jr. Lewis
Publisher :
ISBN 13 : 9783662170328
Total Pages : 552 pages
Book Rating : 4.1/5 (73 download)
Download or read book Equivariant Stable Homotopy Theory written by L. Gaunce Jr. Lewis and published by . This book was released on 2014-01-15 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Anna Marie Riehle Bohmann
Publisher :
ISBN 13 : 9781124717333
Total Pages : 89 pages
Book Rating : 4.7/5 (173 download)
Download or read book Topics in Equivariant Stable Homotopy Theory written by Anna Marie Riehle Bohmann and published by . This book was released on 2011 with total page 89 pages. 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.
Author : Haynes Miller
Publisher : CRC Press
ISBN 13 : 1351251600
Total Pages : 1043 pages
Book Rating : 4.3/5 (512 download)
Download or read book Handbook of Homotopy Theory written by Haynes Miller and published by CRC Press. This book was released on 2020-01-23 with total page 1043 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.
Author : M. A. Mandell
Publisher : American Mathematical Soc.
ISBN 13 : 9780821864777
Total Pages : 132 pages
Book Rating : 4.8/5 (647 download)
Download or read book Equivariant Orthogonal Spectra and S-modules written by M. A. Mandell and published by American Mathematical Soc.. This book was released on 2002-08-19 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last few years have seen a revolution in our understanding of the foundations of stable homotopy theory. Many symmetric monoidal model categories of spectra whose homotopy categories are equivalent to the stable homotopy category are now known, whereas no such categories were known before 1993. The most well-known examples are the category of $S$-modules and the category of symmetric spectra. We focus on the category of orthogonal spectra, which enjoys some of the best features of $S$-modules and symmetric spectra and which is particularly well-suited to equivariant generalization. We first complete the nonequivariant theory by comparing orthogonal spectra to $S$-modules. We then develop the equivariant theory. For a compact Lie group $G$, we construct a symmetric monoidal model category of orthogonal $G$-spectra whose homotopy category is equivalent to the classical stable homotopy category of $G$-spectra. We also complete the theory of $S_G$-modules and compare the categories of orthogonal $G$-spectra and $S_G$-modules. A key feature is the analysis of change of universe, change of group, fixed point, and orbit functors in these two highly structured categories for the study of equivariant stable homotopy theory.
Author : James F. Davis
Publisher : American Mathematical Society
ISBN 13 : 1470473682
Total Pages : 385 pages
Book Rating : 4.4/5 (74 download)
Download or read book Lecture Notes in Algebraic Topology written by James F. Davis and published by American Mathematical Society. This book was released on 2023-05-22 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
Author : Victor P. Snaith
Publisher : Birkhäuser
ISBN 13 : 9783764399344
Total Pages : 239 pages
Book Rating : 4.3/5 (993 download)
Download or read book Stable Homotopy Around the Arf-Kervaire Invariant written by Victor P. Snaith and published by Birkhäuser. This book was released on 2009-08-29 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Were I to take an iron gun, And ?re it o? towards the sun; I grant ‘twould reach its mark at last, But not till many years had passed. But should that bullet change its force, And to the planets take its course, ‘Twould never reach the nearest star, Because it is so very far. from FACTS by Lewis Carroll [55] Let me begin by describing the two purposes which prompted me to write this monograph. This is a book about algebraic topology and more especially about homotopy theory. Since the inception of algebraic topology [217] the study of homotopy classes of continuous maps between spheres has enjoyed a very exc- n n tional, central role. As is well known, for homotopy classes of maps f : S ?? S with n? 1 the sole homotopy invariant is the degree, which characterises the homotopy class completely. The search for a continuous map between spheres of di?erent dimensions and not homotopic to the constant map had to wait for its resolution until the remarkable paper of Heinz Hopf [111]. In retrospect, ?nding 3 an example was rather easy because there is a canonical quotient map from S to 3 1 1 2 theorbitspaceofthe freecircleactionS /S =CP = S .
Author : Giora Dula
Publisher : American Mathematical Soc.
ISBN 13 : 9780821862506
Total Pages : 100 pages
Book Rating : 4.8/5 (625 download)
Download or read book Diagram Cohomology and Isovariant Homotopy Theory written by Giora Dula and published by American Mathematical Soc.. This book was released on with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: In algebraic topology, obstruction theory provides a way to study homotopy classes of continuous maps in terms of cohomology groups; a similar theory exists for certain spaces with group actions and maps that are compatible (that is, equivariant) with respect to the group actions. This work provides a corresponding setting for certain spaces with group actions and maps that are compatible in a stronger sense, called isovariant. The basic idea is to establish an equivalence between isovariant homotopy and equivariant homotopy for certain categories of diagrams. Consequences include isovariant versions of the usual Whitehead theorems for recognizing homotopy equivalences, an obstruction theory for deforming equivariant maps to isovariant maps, rational computations for the homotopy groups of certain spaces of isovariant functions, and applications to constructions and classification problems for differentiable group actions.
Author : Benson Farb
Publisher : American Mathematical Soc.
ISBN 13 : 0821838385
Total Pages : 384 pages
Book Rating : 4.8/5 (218 download)
Download or read book Problems on Mapping Class Groups and Related Topics written by Benson Farb and published by American Mathematical Soc.. This book was released on 2006-09-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.
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.
