Cubical Homotopy Theory PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Cubical Homotopy Theory PDF full book. Access full book title Cubical Homotopy Theory.
Author | : Brian A. Munson |
Publisher | : Cambridge University Press |
Total Pages | : 649 |
Release | : 2015-10-06 |
Genre | : Mathematics |
ISBN | : 1107030250 |
Download Cubical Homotopy Theory Book in PDF, ePub and Kindle
A modern, example-driven introduction to cubical diagrams and related topics such as homotopy limits and cosimplicial spaces.
Author | : Paul Arne Østvær |
Publisher | : Springer Science & Business Media |
Total Pages | : 142 |
Release | : 2010-09-08 |
Genre | : Mathematics |
ISBN | : 303460565X |
Download Homotopy Theory of C*-Algebras Book in PDF, ePub and Kindle
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.
Author | : Ronald Brown |
Publisher | : JP Medical Ltd |
Total Pages | : 714 |
Release | : 2011 |
Genre | : Algebraic topology |
ISBN | : 9783037190838 |
Download Nonabelian Algebraic Topology Book in PDF, ePub and Kindle
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.
Author | : Rosa Antolini |
Publisher | : |
Total Pages | : 0 |
Release | : 1996 |
Genre | : |
ISBN | : |
Download Cubical Structures and Homotopy Theory Book in PDF, ePub and Kindle
Author | : Samuel Baruch Isaacson |
Publisher | : |
Total Pages | : 308 |
Release | : 2009 |
Genre | : |
ISBN | : |
Download Cubical Homotopy Theory and Monoidal Model Categories Book in PDF, ePub and Kindle
Suppose [Special characters omitted.] is a combinatorial symmetric monoidal model category. Dan Dugger has shown that [Special characters omitted.] may be realized as a left Bousfield localization of the projective model structure on simplicial presheaves on a small site. However, if [Special characters omitted.] is not already simplicially enriched, this presentation will not respect the monoidal structure of [Special characters omitted.] . In this paper we will construct a symmetric cubical site [Special characters omitted.] extending the classical cubical site. By replacing the category of simplicial sets with the category of presheaves of sets over [Special characters omitted.] we can use Dugger's methods to produce a presentation of [Special characters omitted.] as presheaves of spaces on a monoidal site retaining the monoidal structure in [Special characters omitted.] as the convolution product.
Author | : Klaus Heiner Kamps |
Publisher | : World Scientific |
Total Pages | : 474 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 9789810216023 |
Download Abstract Homotopy and Simple Homotopy Theory Book in PDF, ePub and Kindle
"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."
Author | : John Vollmer |
Publisher | : |
Total Pages | : 252 |
Release | : 1963 |
Genre | : Homotopy theory |
ISBN | : |
Download Semi-cubical Homotopy Theory of Kan Triads I. Book in PDF, ePub and Kindle
Author | : Georges Gonthier |
Publisher | : |
Total Pages | : 324 |
Release | : 2013-11-20 |
Genre | : |
ISBN | : 9783319035468 |
Download Certified Programs and Proofs Book in PDF, ePub and Kindle
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 | : Hans J. Baues |
Publisher | : Cambridge University Press |
Total Pages | : 490 |
Release | : 1989-02-16 |
Genre | : Mathematics |
ISBN | : 0521333768 |
Download Algebraic Homotopy Book in PDF, ePub and Kindle
This book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed from a few axioms and are thus available in a broad variety of contexts. Many examples and applications in topology and algebra are discussed, including an introduction to rational homotopy theory in terms of both differential Lie algebras and De Rham algebras. The author describes powerful tools for homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group homotopy equivalences. Applications and examples of such computations are given, including when the fundamental group is non-trivial. Moreover, the deep connection between the homotopy classification problems and the cohomology theory of small categories is demonstrated. The prerequisites of the book are few: elementary topology and algebra. Consequently, this account will be valuable for non-specialists and experts alike. It is an important supplement to the standard presentations of algebraic topology, homotopy theory, category theory and homological algebra.