Homotopy theory

relations with algebraic geometry, group cohomology, and algebraic K-theory : an international Conference on Algebraic Topology, March 24-28, 2002, Northwestern University
  • 507 Pages
  • 1.65 MB
  • 4626 Downloads
  • English
by
American Mathematical Society , Providence, R.I
Homotopy theory -- Congresses, Manifolds (Mathematics) -- Congresses, Representations of groups -- Congr
StatementPaul Goerss, Stewart Priddy, editors
GenreCongresses
SeriesContemporary mathematics -- 346, Contemporary mathematics (American Mathematical Society) -- v. 346
ContributionsGoerss, Paul Gregory, Priddy, Stewart, 1940-
Classifications
LC ClassificationsQA612.7 .I68 2002
The Physical Object
Paginationviii, 507 p. :
ID Numbers
Open LibraryOL18163063M
ISBN 100821832859
LC Control Number2004041148

About the book. Homotopy type theory is a new branch of mathematics that combines aspects of several different fields in a surprising way. It is based on a recently discovered connection between homotopy theory and type theory. It touches on topics as seemingly distant Homotopy theory book the homotopy groups of spheres, the algorithms for type checking, and the.

Homotopy type theory offers a new “univalent” foundation of mathematics, in which a central role is played by Voevodsky’s univalence axiom and higher inductive types. The present book is intended as a first systematic exposition of the basics of univalent foundations, and a collection of examples of this new style of reasoning — but /5(3).

Introduction to Homotopy Theory is presented in nine chapters, taking the reader from ‘basic homotopy’ to obstruction theory with a lot of marvelous material in between. Arkowitz’ book is a valuable text and promises to figure prominently in the education of many young topologists.” (Michael Berg, The Mathematical Association of Cited by: ily exist.

In the culmination of the first part of this book, we apply this theory to present a uniform general construction of homotopy limits and colimits which satisfies both a local universal property (representing homotopy coherent cones) and a global one (forming a derived functor).File Size: 1MB.

This book consists of notes for a second year graduate course in advanced topology given by Professor Whitehead at M.I.T. Presupposing a knowledge of the fundamental group and of algebraic topology as far as singular theory, it is designed to introduce the student to some of the more important concepts of homotopy theory.

My book Modal Homotopy Type Theory appears today with Oxford University Press.

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As the subtitle – ‘The prospect of a new logic for philosophy’ – suggests, I’m looking to persuade readers that the kinds of things philosophers look to do with the predicate Homotopy theory book, set theory and modal logic are better achieved by modal homotopy (dependent) type theory.

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. 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 : David Barnes, Constanze Roitzheim.

This is a textbook on informal homotopy type theory. It is part of the Univalent foundations of mathematics project that took Homotopy theory book at the Institute for Advanced Study in / License. This work is licensed under the Creative Commons Attribution-ShareAlike Unported License.

Distribution. Compiled and printed versions of the book are available at the homotopy type theory website, and. Working with these is a lot of fun and I have been doing many of the proofs in synthetic homotopy theory from the HoTT book cubically.

Having a system with native support for HITs makes many things a lot easier and most of the proofs I have done are significantly shorter.

A book published on Decem by Chapman and Hall/CRC (ISBN ), pages. Haynes Miller (ed.) Handbook of Homotopy Theory (table of contents) on homotopy theory, including higher algebra and higher category theory. Terminology. The editor, Haynes Miller, comments in the introduction on the choice of title.

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 : Birgit Richter.

Introduction to Homotopy Theory is presented in nine chapters, taking the reader from ‘basic homotopy’ to obstruction theory with a lot of marvelous material in between.

Arkowitz’ book is a valuable text and promises to figure prominently in the education of many young topologists.” (Michael Berg, The Mathematical Association of. Modal Homotopy Type Theory The Prospect of a New Logic for Philosophy David Corfield.

The first book-length philosophical treatment of homotopy type theory, and its modal variants; With applications in language, metaphysics and mathematics, the reader is shown the power of the new language. 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. so I will be grateful if someone could recommend me a book with the following structure.

Introduction to basic homotopy theory (derive category and t-structure) uction to sheaves. Introduction to perverse sheaves ; Thanks you in advance.

This book provides an introduction to the basic concepts and methods of algebraic topology for the beginner. It presents elements of both homology theory and homotopy theory, and includes various applications. The author's intention is to rely on the geometric approach by appealing to the reader's own intuition to help understanding.

The language and basic theory of homotopy limits and colimits make it possible to penetrate deep into the subject with just the rudiments of algebra. The text does reach advanced territory, including the Steenrod algebra, Bott periodicity, localization, the Exponent Theorem of Cohen, Moore, and Neisendorfer, and Miller's Theorem on the Sullivan.

HOMOTOPY THEORY FOR BEGINNERS JESPER M. M˜LLER Abstract. This note contains comments to Chapter 0 in Allan Hatcher’s book [5]. Contents 1. Notation and some standard spaces and constructions1 Standard topological spaces1 The quotient topology 2 The category of topological spaces and continuous maps3 2.

Homotopy 4 Relative File Size: KB. algebra”. Homotopy pullbacks and pushouts lie at the core of much of what we do and they build a foundation for the homotopy theory of cubical dia-grams, which in turn provides a concrete introduction to the theory of general homotopy(co)limits and (co)simplicial spaces.

Features. We develop the homotopy theory of cubical diagrams in a gradual. another on Goodwillie calculus. But in the book that emerged it seemed thematically appropriate to draw the line at stable homotopy theory, so space and thematic consistency drove these chapters to the cutting room floor.

Problems and Exercises. Many authors of textbooks assert that the only way to learn the subject is to do the Size: 1MB. 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. Algebraic Methods in Unstable Homotopy Theory This is a comprehensive up-to-date treatment of unstable homotopy.

The focus is on those methods from algebraic topology which are needed in the presentation of results, proven by Cohen, Moore, and the author, on the exponents of homotopy groups. Vector Bundles and K-Theory. This unfinished book is intended to be a fairly short introduction to topological K-theory, starting with the necessary background material on vector bundles and including also basic material on characteristic classes.

For further information or to download the part of the book that is written, go to the download page. Another great reference is Hovey-Shipley-Smith Symmetric Spectra. On the more modern side, there's Stefan Schwede's Symmetric Spectra Book Project.

All these references contain phrasing in terms of model categories, which seem indispensible to modern homotopy theory. Good references are Hovey's book and Hirschhorn's book. Book The course notes that I took are evolving into an introductory textbook for students who want to learn homotopy type theory for the first time.

They are currently subject to frequent change, so my recommendation would be to have a look at the course notes or.

Details Homotopy theory PDF

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 Price: $ This book consists of notes for a second-year graduate course in advanced topology given by Professor Whitehead at M.I.T.

Presupposing a knowledge of the fundamental group and of algebraic topology as far as singular theory, it is designed to introduce the student to some of the more important concepts of homotopy theory.

Description Homotopy theory EPUB

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. Homotopy type theory is a new branch of mathematics that combines aspects of several different fields in a surprising way. It is based on a recently discovered /5.

Homotopy theory. [S T Hu] -- The recognition of the branch of mathematics now known as homotopy theory occurred a few years after the introduction of homotopy groups by Witold Hurewicz in This book is designed for the beginning student or newcomer to this branch of mathematics--who has a little knowledge of algebraic topology--to be.

The first six chapters describe the essential ideas of homotopy theory: homotopy groups, the classical theorems, the exact homotopy sequence, fibre-spaces, the Hopf invariant, and the Freudenthal suspension. The final chapters discuss J.

H. C. Whitehead's cell-complexes and their application to homotopy groups of : $  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 Edition: 1.