Cubical Homotopy Theory
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Cubical Homotopy Theory
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Author : Brian A. Munson
language : en
Publisher: Cambridge University Press
Release Date : 2015-10-06
Cubical Homotopy Theory written by Brian A. Munson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-06 with Mathematics categories.
A modern, example-driven introduction to cubical diagrams and related topics such as homotopy limits and cosimplicial spaces.
Nonabelian Algebraic Topology
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Author : Ronald Brown
language : en
Publisher: JP Medical Ltd
Release Date : 2011
Nonabelian Algebraic Topology written by Ronald Brown and has been published by JP Medical Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Algebraic topology categories.
The main theme of this book is that the use of filtered spaces rather than just topological spaces allows the development of basic algebraic topology in terms of higher homotopy groupoids; these algebraic structures better reflect the geometry of subdivision and composition than those commonly in use. Exploration of these uses of higher dimensional versions of groupoids has been largely the work of the first two authors since the mid 1960s. The structure of the book is intended to make it useful to a wide class of students and researchers for learning and evaluating these methods, primarily in algebraic topology but also in higher category theory and its applications in analogous areas of mathematics, physics, and computer science. Part I explains the intuitions and theory in dimensions 1 and 2, with many figures and diagrams, and a detailed account of the theory of crossed modules. Part II develops the applications of crossed complexes. The engine driving these applications is the work of Part III on cubical $\omega$-groupoids, their relations to crossed complexes, and their homotopically defined examples for filtered spaces. Part III also includes a chapter suggesting further directions and problems, and three appendices give accounts of some relevant aspects of category theory. Endnotes for each chapter give further history and references.
Homotopy Theory Of C Algebras
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Author : Paul Arne Østvær
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-08
Homotopy Theory Of C Algebras written by Paul Arne Østvær and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-08 with Mathematics categories.
Homotopy theory and C* algebras are central topics in contemporary mathematics. This book introduces a modern homotopy theory for C*-algebras. One basic idea of the setup is to merge C*-algebras and spaces studied in algebraic topology into one category comprising C*-spaces. These objects are suitable fodder for standard homotopy theoretic moves, leading to unstable and stable model structures. With the foundations in place one is led to natural definitions of invariants for C*-spaces such as homology and cohomology theories, K-theory and zeta-functions. The text is largely self-contained. It serves a wide audience of graduate students and researchers interested in C*-algebras, homotopy theory and applications.
Abstract Homotopy And Simple Homotopy Theory
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Author : K Heiner Kamps
language : en
Publisher: World Scientific
Release Date : 1997-04-11
Abstract Homotopy And Simple Homotopy Theory written by K Heiner Kamps and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-04-11 with Mathematics categories.
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).
Homotopy Theory
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Author : George William Whitehead
language : en
Publisher:
Release Date : 1966
Homotopy Theory written by George William Whitehead and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Homotopy theory categories.
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. The book emphasizes (relative) CW-complexes, which the author believes to be the natural setting for obstruction theory, and follows the spirit of J.H.C. Whitehead's "combinatorial homotopy".
Homotopy Theory
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Author :
language : en
Publisher: Academic Press
Release Date : 1959-01-01
Homotopy Theory written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959-01-01 with Mathematics categories.
Homotopy Theory
Lectures On Homotopy Theory
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Author : R.A. Piccinini
language : en
Publisher: Elsevier
Release Date : 1992-01-21
Lectures On Homotopy Theory written by R.A. Piccinini and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-21 with Mathematics categories.
The central idea of the lecture course which gave birth to this book was to define the homotopy groups of a space and then give all the machinery needed to prove in detail that the nth homotopy group of the sphere Sn, for n greater than or equal to 1 is isomorphic to the group of the integers, that the lower homotopy groups of Sn are trivial and that the third homotopy group of S2 is also isomorphic to the group of the integers. All this was achieved by discussing H-spaces and CoH-spaces, fibrations and cofibrations (rather thoroughly), simplicial structures and the homotopy groups of maps. Later, the book was expanded to introduce CW-complexes and their homotopy groups, to construct a special class of CW-complexes (the Eilenberg-Mac Lane spaces) and to include a chapter devoted to the study of the action of the fundamental group on the higher homotopy groups and the study of fibrations in the context of a category in which the fibres are forced to live; the final material of that chapter is a comparison of various kinds of universal fibrations. Completing the book are two appendices on compactly generated spaces and the theory of colimits. The book does not require any prior knowledge of Algebraic Topology and only rudimentary concepts of Category Theory are necessary; however, the student is supposed to be well at ease with the main general theorems of Topology and have a reasonable mathematical maturity.
Algebraic Topology A Structural Introduction
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Author : Marco Grandis
language : en
Publisher: World Scientific
Release Date : 2021-12-24
Algebraic Topology A Structural Introduction written by Marco Grandis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-24 with Mathematics categories.
Algebraic Topology is a system and strategy of partial translations, aiming to reduce difficult topological problems to algebraic facts that can be more easily solved. The main subject of this book is singular homology, the simplest of these translations. Studying this theory and its applications, we also investigate its underlying structural layout - the topics of Homological Algebra, Homotopy Theory and Category Theory which occur in its foundation.This book is an introduction to a complex domain, with references to its advanced parts and ramifications. It is written with a moderate amount of prerequisites — basic general topology and little else — and a moderate progression starting from a very elementary beginning. A consistent part of the exposition is organised in the form of exercises, with suitable hints and solutions.It can be used as a textbook for a semester course or self-study, and a guidebook for further study.
Rational Homotopy Theory And Differential Forms
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Author : Phillip Griffiths
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-02
Rational Homotopy Theory And Differential Forms written by Phillip Griffiths and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-02 with Mathematics categories.
This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham’s theorem on simplicial complexes. In addition, Sullivan’s results on computing the rational homotopy type from forms is presented. New to the Second Edition: *Fully-revised appendices including an expanded discussion of the Hirsch lemma *Presentation of a natural proof of a Serre spectral sequence result *Updated content throughout the book, reflecting advances in the area of homotopy theory With its modern approach and timely revisions, this second edition of Rational Homotopy Theory and Differential Forms will be a valuable resource for graduate students and researchers in algebraic topology, differential forms, and homotopy theory.
Abstract Homotopy And Simple Homotopy Theory
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Author : Klaus Heiner Kamps
language : en
Publisher: World Scientific
Release Date : 1997
Abstract Homotopy And Simple Homotopy Theory written by Klaus Heiner Kamps and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
"This book provides a thorough and well-written guide to abstract homotopy theory. It could well serve as a graduate text in this topic, or could be studied independently by someone with a background in basic algebra, topology, and category theory."