Read Books Online and Download eBooks, EPub, PDF, Mobi, Kindle, Text Full Free.
Parametrized Homotopy Theory
Download Parametrized Homotopy Theory full books in PDF, epub, and Kindle. Read online Parametrized Homotopy Theory ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis Parametrized Homotopy Theory by : J. Peter May
Download or read book Parametrized Homotopy Theory written by J. Peter May and published by American Mathematical Soc.. This book was released on 2006 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops rigorous foundations for parametrized homotopy theory, which is the algebraic topology of spaces and spectra that are continuously parametrized by the points of a base space. It also begins the systematic study of parametrized homology and cohomology theories. The parametrized world provides the natural home for many classical notions and results, such as orientation theory, the Thom isomorphism, Atiyah and Poincare duality, transfer maps, the Adams and Wirthmuller isomorphisms, and the Serre and Eilenberg-Moore spectral sequences. But in addition to providing a clearer conceptual outlook on these classical notions, it also provides powerful methods to study new phenomena, such as twisted $K$-theory, and to make new constructions, such as iterated Thom spectra. Duality theory in the parametrized setting is particularly illuminating and comes in two flavors. One allows the construction and analysis of transfer maps, and a quite different one relates parametrized homology to parametrized cohomology. The latter is based formally on a new theory of duality in symmetric bicategories that is of considerable independent interest. The text brings together many recent developments in homotopy theory. It provides a highly structured theory of parametrized spectra, and it extends parametrized homotopy theory to the equivariant setting. The theory of topological model categories is given a more thorough treatment than is available in the literature. This is used, together with an interesting blend of classical methods, to resolve basic foundational problems that have no nonparametrized counterparts.
Book Synopsis New Directions in Homotopy Theory by : Nitya Kitchloo, Mona Merling
Download or read book New Directions in Homotopy Theory written by Nitya Kitchloo, Mona Merling and published by American Mathematical Soc.. This book was released on 2018-05-29 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Second Mid-Atlantic Topology Conference, held from March 12–13, 2016, at Johns Hopkins University in Baltimore, Maryland. The focus of the conference, and subsequent papers, was on applications of innovative methods from homotopy theory in category theory, algebraic geometry, and related areas, emphasizing the work of younger researchers in these fields.
Book Synopsis Categorical Homotopy Theory by : Emily Riehl
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.
Book Synopsis Fixed Point Theory of Parametrized Equivariant Maps by : Hanno Ulrich
Download or read book Fixed Point Theory of Parametrized Equivariant Maps written by Hanno Ulrich and published by Springer. This book was released on 2006-11-15 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this research monograph discusses general properties of G-ENRBs - Euclidean Neighbourhood Retracts over B with action of a compact Lie group G - and their relations with fibrations, continuous submersions, and fibre bundles. It thus addresses equivariant point set topology as well as equivariant homotopy theory. Notable tools are vertical Jaworowski criterion and an equivariant transversality theorem. The second part presents equivariant cohomology theory showing that equivariant fixed point theory is isomorphic to equivariant stable cohomotopy theory. A crucial result is the sum decomposition of the equivariant fixed point index which provides an insight into the structure of the theory's coefficient group. Among the consequences of the sum formula are some Borsuk-Ulam theorems as well as some folklore results on compact Lie-groups. The final section investigates the fixed point index in equivariant K-theory. The book is intended to be a thorough and comprehensive presentation of its subject. The reader should be familiar with the basics of the theory of compact transformation groups. Good knowledge of algebraic topology - both homotopy and homology theory - is assumed. For the advanced reader, the book may serve as a base for further research. The student will be introduced into equivariant fixed point theory; he may find it helpful for further orientation.
Book Synopsis Foundations of Stable Homotopy Theory by : David Barnes
Download or read book Foundations of Stable Homotopy Theory written by David Barnes and published by Cambridge University Press. This book was released on 2020-03-26 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The beginning graduate student in homotopy theory is confronted with a vast literature on spectra that is scattered across books, articles and decades. There is much folklore but very few easy entry points. This comprehensive introduction to stable homotopy theory changes that. It presents the foundations of the subject together in one place for the first time, from the motivating phenomena to the modern theory, at a level suitable for those with only a first course in algebraic topology. Starting from stable homotopy groups and (co)homology theories, the authors study the most important categories of spectra and the stable homotopy category, before moving on to computational aspects and more advanced topics such as monoidal structures, localisations and chromatic homotopy theory. The appendix containing essential facts on model categories, the numerous examples and the suggestions for further reading make this a friendly introduction to an often daunting subject.
Book Synopsis Equivariant Ordinary Homology and Cohomology by : Steven R. Costenoble
Download or read book Equivariant Ordinary Homology and Cohomology written by Steven R. Costenoble and published by Springer. This book was released on 2017-01-02 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Filling a gap in the literature, this book takes the reader to the frontiers of equivariant topology, the study of objects with specified symmetries. The discussion is motivated by reference to a list of instructive “toy” examples and calculations in what is a relatively unexplored field. The authors also provide a reading path for the first-time reader less interested in working through sophisticated machinery but still desiring a rigorous understanding of the main concepts. The subject’s classical counterparts, ordinary homology and cohomology, dating back to the work of Henri Poincaré in topology, are calculational and theoretical tools which are important in many parts of mathematics and theoretical physics, particularly in the study of manifolds. Similarly powerful tools have been lacking, however, in the context of equivariant topology. Aimed at advanced graduate students and researchers in algebraic topology and related fields, the book assumes knowledge of basic algebraic topology and group actions.
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 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.
Book Synopsis Global Homotopy Theory by : Stefan Schwede
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.
Book Synopsis Categorical Homotopy Theory by : Emily Riehl
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 categorical perspective on homotopy theory helps consolidate and simplify one's understanding of derived functors, homotopy limits and colimits, and model categories, among others.
Book Synopsis Handbook of Homotopy Theory by : Haynes Miller
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.
Book Synopsis Global Homotopy Theory by : Stefan Schwede
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 847 pages. 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.
Book Synopsis Cubical Homotopy Theory by : Brian A. Munson
Download or read book Cubical Homotopy Theory written by Brian A. Munson and published by Cambridge University Press. This book was released on 2015-10-06 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern, example-driven introduction to cubical diagrams and related topics such as homotopy limits and cosimplicial spaces.
Book Synopsis Representation Theory and Beyond by : Jan Šťovíček
Download or read book Representation Theory and Beyond written by Jan Šťovíček and published by American Mathematical Soc.. This book was released on 2020-11-13 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Workshop and 18th International Conference on Representations of Algebras (ICRA 2018) held from August 8–17, 2018, in Prague, Czech Republic. It presents several themes of contemporary representation theory together with some new tools, such as stable ∞ ∞-categories, stable derivators, and contramodules. In the first part, expanded lecture notes of four courses delivered at the workshop are presented, covering the representation theory of finite sets with correspondences, geometric theory of quiver Grassmannians, recent applications of contramodules to tilting theory, as well as symmetries in the representation theory over an abstract stable homotopy theory. The second part consists of six more-advanced papers based on plenary talks of the conference, presenting selected topics from contemporary representation theory: recollements and purity, maximal green sequences, cohomological Hall algebras, Hochschild cohomology of associative algebras, cohomology of local selfinjective algebras, and the higher Auslander–Reiten theory studied via homotopy theory.
Download or read book The ?ech Centennial written by Mila Cenkl and published by American Mathematical Soc.. This book was released on 1995 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the refereed proceedings of the %Cech Centennial Homotopy Theory Conference, organized to commemorate the 100th anniversary of the birth of Eduard %Cech and held at Northeastern University in June 1993. Focusing on the theme of stable and unstable homotopy theory, the conference attracted more than one hundred mathematicians from around the world. With recent results by some of the leaders in the field, this book will provide readers with a look at important directions in current research in homotopy theory.
Book Synopsis Bousfield Classes and Ohkawa's Theorem by : Takeo Ohsawa
Download or read book Bousfield Classes and Ohkawa's Theorem written by Takeo Ohsawa and published by Springer Nature. This book was released on 2020-03-18 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume originated in the workshop held at Nagoya University, August 28–30, 2015, focusing on the surprising and mysterious Ohkawa's theorem: the Bousfield classes in the stable homotopy category SH form a set. An inspiring, extensive mathematical story can be narrated starting with Ohkawa's theorem, evolving naturally with a chain of motivational questions: Ohkawa's theorem states that the Bousfield classes of the stable homotopy category SH surprisingly forms a set, which is still very mysterious. Are there any toy models where analogous Bousfield classes form a set with a clear meaning? The fundamental theorem of Hopkins, Neeman, Thomason, and others states that the analogue of the Bousfield classes in the derived category of quasi-coherent sheaves Dqc(X) form a set with a clear algebro-geometric description. However, Hopkins was actually motivated not by Ohkawa's theorem but by his own theorem with Smith in the triangulated subcategory SHc, consisting of compact objects in SH. Now the following questions naturally occur: (1) Having theorems of Ohkawa and Hopkins-Smith in SH, are there analogues for the Morel-Voevodsky A1-stable homotopy category SH(k), which subsumes SH when k is a subfield of C?, (2) Was it not natural for Hopkins to have considered Dqc(X)c instead of Dqc(X)? However, whereas there is a conceptually simple algebro-geometrical interpretation Dqc(X)c = Dperf(X), it is its close relative Dbcoh(X) that traditionally, ever since Oka and Cartan, has been intensively studied because of its rich geometric and physical information. This book contains developments for the rest of the story and much more, including the chromatics homotopy theory, which the Hopkins–Smith theorem is based upon, and applications of Lurie's higher algebra, all by distinguished contributors.
Book Synopsis Homotopy Theory and Related Topics by : Hiroshi Toda
Download or read book Homotopy Theory and Related Topics written by Hiroshi Toda and published by . This book was released on 1987 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume are divided into the following four parts: 1. Simple homotopy theory and G-actions. 2. Classifying spaces and characteristic classes. 3. Topology of manifolds. 4. Homotopy problems - unstable and stable cases.
Book Synopsis Category Theory And Applications: A Textbook For Beginners (Second Edition) by : Marco Grandis
Download or read book Category Theory And Applications: A Textbook For Beginners (Second Edition) written by Marco Grandis and published by World Scientific. This book was released on 2021-03-05 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a better understanding of their roots.This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers the basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications.A reader should have some elementary knowledge of these three subjects, or at least two of them, in order to be able to follow the main examples, appreciate the unifying power of the categorical approach, and discover the subterranean links brought to light and formalised by this perspective.Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications in Algebra and Topology, with a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.In this second edition, the book has been entirely reviewed, adding many applications and exercises. All non-obvious exercises have now a solution (or a reference, in the case of an advanced topic); solutions are now collected in the last chapter.
