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Author: Brian A. Munson
Publisher: Cambridge University Press
Published: 2015-10-06
Total Pages: 649
ISBN-13: 1107030250
DOWNLOAD EBOOK →A modern, example-driven introduction to cubical diagrams and related topics such as homotopy limits and cosimplicial spaces.
Author: Ronald Brown
Publisher: JP Medical Ltd
Published: 2011
Total Pages: 714
ISBN-13: 9783037190838
DOWNLOAD EBOOK →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: Paul Arne Østvær
Publisher: Springer Science & Business Media
Published: 2010-09-08
Total Pages: 142
ISBN-13: 303460565X
DOWNLOAD EBOOK →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: Georges Gonthier
Publisher:
Published: 2013-11-20
Total Pages: 324
ISBN-13: 9783319035468
DOWNLOAD EBOOK →Author: Hans J. Baues
Publisher: Cambridge University Press
Published: 1989-02-16
Total Pages: 490
ISBN-13: 0521333768
DOWNLOAD EBOOK →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.
Author: Klaus Heiner Kamps
Publisher: World Scientific
Published: 1997
Total Pages: 474
ISBN-13: 9789810216023
DOWNLOAD EBOOK →"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: K Heiner Kamps
Publisher: World Scientific
Published: 1997-04-11
Total Pages: 476
ISBN-13: 9814502553
DOWNLOAD EBOOK →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).
Author: Michael A. Hill
Publisher: Cambridge University Press
Published: 2021-07-29
Total Pages: 881
ISBN-13: 1108831443
DOWNLOAD EBOOK →A complete and definitive account of the authors' resolution of the Kervaire invariant problem in stable homotopy theory.
Author: Eraldo Giuli
Publisher: Springer Science & Business Media
Published: 1996-06-30
Total Pages: 294
ISBN-13: 9780792340492
DOWNLOAD EBOOK →This volume contains selected papers presented at the International Workshop on Categorical Topology, held at the University of L'Aquila, L'Aquila, Italy from August 31 to September 4, 1994. The collection should be of interest to mathematicians whose work involves category theory.
