Handbook Of Homotopy Theory

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Handbook of Homotopy Theory

Author : Haynes Miller
Publisher : CRC Press
ISBN 13 : 1351251600
Total Pages : 1043 pages
Book Rating : 4.3/5 (512 download)

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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.

Handbook of Algebraic Topology

Author : I.M. James
Publisher : Elsevier
ISBN 13 : 9780080532981
Total Pages : 1324 pages
Book Rating : 4.5/5 (329 download)

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Book Synopsis Handbook of Algebraic Topology by : I.M. James

Download or read book Handbook of Algebraic Topology written by I.M. James and published by Elsevier. This book was released on 1995-07-18 with total page 1324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Homotopy Type Theory: Univalent Foundations of Mathematics

Author :
Publisher : Univalent Foundations
ISBN 13 :
Total Pages : 484 pages
Book Rating : 4./5 ( download)

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Book Synopsis Homotopy Type Theory: Univalent Foundations of Mathematics by :

Download or read book Homotopy Type Theory: Univalent Foundations of Mathematics written by and published by Univalent Foundations. This book was released on with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Homotopy Theory

Author : Paul Selick
Publisher : American Mathematical Soc.
ISBN 13 : 9780821844366
Total Pages : 220 pages
Book Rating : 4.8/5 (443 download)

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Book Synopsis Introduction to Homotopy Theory by : Paul Selick

Download or read book Introduction to Homotopy Theory written by Paul Selick and published by American Mathematical Soc.. This book was released on 2008 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a summary for students and non-specialists who are interested in learning the basics of algebraic topology. This book covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, and generalized homology and cohomology operations.

A Handbook of Model Categories

Author : Scott Balchin
Publisher : Springer Nature
ISBN 13 : 3030750353
Total Pages : 326 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis A Handbook of Model Categories by : Scott Balchin

Download or read book A Handbook of Model Categories written by Scott Balchin and published by Springer Nature. This book was released on 2021-10-29 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem

Author : Michael A. Hill
Publisher : Cambridge University Press
ISBN 13 : 1108831443
Total Pages : 881 pages
Book Rating : 4.1/5 (88 download)

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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.

From Categories to Homotopy Theory

Author : Birgit Richter
Publisher : Cambridge University Press
ISBN 13 : 1108847625
Total Pages : 402 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis From Categories to Homotopy Theory by : Birgit Richter

Download or read book From Categories to Homotopy Theory written by Birgit Richter and published by Cambridge University Press. This book was released on 2020-04-16 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.

Handbook of Homotopy Theory

Author : Haynes Miller
Publisher : CRC Press
ISBN 13 : 1351251619
Total Pages : 982 pages
Book Rating : 4.3/5 (512 download)

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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 982 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.

Handbook of Tilting Theory

Author : Lidia Angeleri Hügel
Publisher : Cambridge University Press
ISBN 13 : 9780521680455
Total Pages : 482 pages
Book Rating : 4.6/5 (84 download)

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Book Synopsis Handbook of Tilting Theory by : Lidia Angeleri Hügel

Download or read book Handbook of Tilting Theory written by Lidia Angeleri Hügel and published by Cambridge University Press. This book was released on 2007-01-04 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: A handbook of key articles providing both an introduction and reference for newcomers and experts alike.

Motivic Homotopy Theory

Author : Bjorn Ian Dundas
Publisher : Springer Science & Business Media
ISBN 13 : 3540458972
Total Pages : 228 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Motivic Homotopy Theory by : Bjorn Ian Dundas

Download or read book Motivic Homotopy Theory written by Bjorn Ian Dundas and published by Springer Science & Business Media. This book was released on 2007-07-11 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures On Algebraic Topology

Author : Haynes R Miller
Publisher : World Scientific
ISBN 13 : 9811231265
Total Pages : 405 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Lectures On Algebraic Topology by : Haynes R Miller

Download or read book Lectures On Algebraic Topology written by Haynes R Miller and published by World Scientific. This book was released on 2021-09-20 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and student-friendly, but precise. Every lecture is accompanied by exercises. It begins slowly in order to gather up students with a variety of backgrounds, but gains pace as the course progresses, and by the end the student has a command of all the basic techniques of classical homotopy theory.

A Concise Course in Algebraic Topology

Author : J. P. May
Publisher : University of Chicago Press
ISBN 13 : 9780226511832
Total Pages : 262 pages
Book Rating : 4.5/5 (118 download)

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Book Synopsis A Concise Course in Algebraic Topology by : J. P. May

Download or read book A Concise Course in Algebraic Topology written by J. P. May and published by University of Chicago Press. This book was released on 1999-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.

Introduction to Homotopy Theory

Author : Martin Arkowitz
Publisher : Springer Science & Business Media
ISBN 13 : 144197329X
Total Pages : 344 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Introduction to Homotopy Theory by : Martin Arkowitz

Download or read book Introduction to Homotopy Theory written by Martin Arkowitz and published by Springer Science & Business Media. This book was released on 2011-07-25 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology. The principal topics are as follows: Basic Homotopy; H-spaces and co-H-spaces; fibrations and cofibrations; exact sequences of homotopy sets, actions, and coactions; homotopy pushouts and pullbacks; classical theorems, including those of Serre, Hurewicz, Blakers-Massey, and Whitehead; homotopy Sets; homotopy and homology decompositions of spaces and maps; and obstruction theory. The underlying theme of the entire book is the Eckmann-Hilton duality theory. The book can be used as a text for the second semester of an advanced ungraduate or graduate algebraic topology course.

Abstract Homotopy And Simple Homotopy Theory

Author : K Heiner Kamps
Publisher : World Scientific
ISBN 13 : 9814502553
Total Pages : 476 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Abstract Homotopy And Simple Homotopy Theory by : K Heiner Kamps

Download or read book Abstract Homotopy And Simple Homotopy Theory written by K Heiner Kamps and published by World Scientific. This book was released on 1997-04-11 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The abstract homotopy theory is based on the observation that analogues of much of the topological homotopy theory and simple homotopy theory exist in many other categories (e.g. spaces over a fixed base, groupoids, chain complexes, module categories). Studying categorical versions of homotopy structure, such as cylinders and path space constructions, enables not only a unified development of many examples of known homotopy theories but also reveals the inner working of the classical spatial theory. This demonstrates the logical interdependence of properties (in particular the existence of certain Kan fillers in associated cubical sets) and results (Puppe sequences, Vogt's Iemma, Dold's theorem on fibre homotopy equivalences, and homotopy coherence theory).

Categories for the Working Mathematician

Author : Saunders Mac Lane
Publisher : Springer Science & Business Media
ISBN 13 : 1475747217
Total Pages : 320 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Categories for the Working Mathematician by : Saunders Mac Lane

Download or read book Categories for the Working Mathematician written by Saunders Mac Lane and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.

Handbook of Mathematics

Author : Vialar Thierry
Publisher : BoD - Books on Demand
ISBN 13 : 2955199052
Total Pages : 1134 pages
Book Rating : 4.9/5 (551 download)

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Book Synopsis Handbook of Mathematics by : Vialar Thierry

Download or read book Handbook of Mathematics written by Vialar Thierry and published by BoD - Books on Demand. This book was released on 2023-08-22 with total page 1134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book, revised, consists of XI Parts and 28 Chapters covering all areas of mathematics. It is a tool for students, scientists, engineers, students of many disciplines, teachers, professionals, writers and also for a general reader with an interest in mathematics and in science. It provides a wide range of mathematical concepts, definitions, propositions, theorems, proofs, examples, and numerous illustrations. The difficulty level can vary depending on chapters, and sustained attention will be required for some. The structure and list of Parts are quite classical: I. Foundations of Mathematics, II. Algebra, III. Number Theory, IV. Geometry, V. Analytic Geometry, VI. Topology, VII. Algebraic Topology, VIII. Analysis, IX. Category Theory, X. Probability and Statistics, XI. Applied Mathematics. Appendices provide useful lists of symbols and tables for ready reference. Extensive cross-references allow readers to find related terms, concepts and items (by page number, heading, and objet such as theorem, definition, example, etc.). The publisher’s hope is that this book, slightly revised and in a convenient format, will serve the needs of readers, be it for study, teaching, exploration, work, or research.

A User's Guide to Spectral Sequences

Author : John McCleary
Publisher : Cambridge University Press
ISBN 13 : 0521567599
Total Pages : 579 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis A User's Guide to Spectral Sequences by : John McCleary

Download or read book A User's Guide to Spectral Sequences written by John McCleary and published by Cambridge University Press. This book was released on 2001 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.