Handbook Of Homotopy Theory PDF Download
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Author | : Haynes Miller |
Publisher | : CRC Press |
Total Pages | : 982 |
Release | : 2020-01-23 |
Genre | : Mathematics |
ISBN | : 1351251619 |
Download Handbook of Homotopy Theory Book in PDF, ePub and Kindle
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 | : I.M. James |
Publisher | : Elsevier |
Total Pages | : 1336 |
Release | : 1995-07-18 |
Genre | : Mathematics |
ISBN | : 0080532985 |
Download Handbook of Algebraic Topology Book in PDF, ePub and Kindle
Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up-to-date overview of this exciting branch of mathematics.
Author | : |
Publisher | : Univalent Foundations |
Total Pages | : 484 |
Release | : |
Genre | : |
ISBN | : |
Download Homotopy Type Theory: Univalent Foundations of Mathematics Book in PDF, ePub and Kindle
Author | : Scott Balchin |
Publisher | : Springer Nature |
Total Pages | : 326 |
Release | : 2021-10-29 |
Genre | : Mathematics |
ISBN | : 3030750353 |
Download A Handbook of Model Categories Book in PDF, ePub and Kindle
This book outlines a vast array of techniques and methods regarding model categories, without focussing on the intricacies of the proofs. Quillen model categories are a fundamental tool for the understanding of homotopy theory. While many introductions to model categories fall back on the same handful of canonical examples, the present book highlights a large, self-contained collection of other examples which appear throughout the literature. In particular, it collects a highly scattered literature into a single volume. The book is aimed at anyone who uses, or is interested in using, model categories to study homotopy theory. It is written in such a way that it can be used as a reference guide for those who are already experts in the field. However, it can also be used as an introduction to the theory for novices.
Author | : Emily Riehl |
Publisher | : Cambridge University Press |
Total Pages | : 371 |
Release | : 2014-05-26 |
Genre | : Mathematics |
ISBN | : 1139952633 |
Download Categorical Homotopy Theory Book in PDF, ePub and Kindle
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 | : |
Publisher | : |
Total Pages | : |
Release | : 1995 |
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ISBN | : |
Download Handbook of algebraic topology Book in PDF, ePub and Kindle
Presents information on the "Handbook of Algebraic Topology," published by Elsevier Science. Includes a foreword, a list of contributors, and a subject index. Provides access to related journals and offers ordering information. Posts contact information via mailing address, telephone and fax numbers, and e-mail. Notes that algebraic topology, also known as homotopy theory, is a branch of modern mathematics.
Author | : George W. Whitehead |
Publisher | : Springer Science & Business Media |
Total Pages | : 764 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461263182 |
Download Elements of Homotopy Theory Book in PDF, ePub and Kindle
As the title suggests, this book is concerned with the elementary portion of the subject of homotopy theory. It is assumed that the reader is familiar with the fundamental group and with singular homology theory, including the Universal Coefficient and Kiinneth Theorems. Some acquaintance with manifolds and Poincare duality is desirable, but not essential. Anyone who has taught a course in algebraic topology is familiar with the fact that a formidable amount of technical machinery must be introduced and mastered before the simplest applications can be made. This phenomenon is also observable in the more advanced parts of the subject. I have attempted to short-circuit it by making maximal use of elementary methods. This approach entails a leisurely exposition in which brevity and perhaps elegance are sacrificed in favor of concreteness and ease of application. It is my hope that this approach will make homotopy theory accessible to workers in a wide range of other subjects-subjects in which its impact is beginning to be felt. It is a consequence of this approach that the order of development is to a certain extent historical. Indeed, if the order in which the results presented here does not strictly correspond to that in which they were discovered, it nevertheless does correspond to an order in which they might have been discovered had those of us who were working in the area been a little more perspicacious.
Author | : Michael A. Hill |
Publisher | : Cambridge University Press |
Total Pages | : 881 |
Release | : 2021-07-29 |
Genre | : Mathematics |
ISBN | : 1108831443 |
Download Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem Book in PDF, ePub and Kindle
A complete and definitive account of the authors' resolution of the Kervaire invariant problem in stable homotopy theory.
Author | : Bjorn Ian Dundas |
Publisher | : Springer Science & Business Media |
Total Pages | : 228 |
Release | : 2007-07-11 |
Genre | : Mathematics |
ISBN | : 3540458972 |
Download Motivic Homotopy Theory Book in PDF, ePub and Kindle
This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.
Author | : Lidia Angeleri Hügel |
Publisher | : Cambridge University Press |
Total Pages | : 482 |
Release | : 2007-01-04 |
Genre | : Mathematics |
ISBN | : 9780521680455 |
Download Handbook of Tilting Theory Book in PDF, ePub and Kindle
A handbook of key articles providing both an introduction and reference for newcomers and experts alike.