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.
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.
Categorical Topology
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Author : Eraldo Giuli
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-06-30
Categorical Topology written by Eraldo Giuli 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 1996-06-30 with Mathematics categories.
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.
Handbook Of Homotopy Theory
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Author : Haynes Miller
language : en
Publisher: CRC Press
Release Date : 2020-01-23
Handbook Of Homotopy Theory written by Haynes Miller and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-23 with Mathematics categories.
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.
Equivariant Stable Homotopy Theory And The Kervaire Invariant Problem
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Author : Michael A. Hill
language : en
Publisher: Cambridge University Press
Release Date : 2021-07-29
Equivariant Stable Homotopy Theory And The Kervaire Invariant Problem written by Michael A. Hill 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 2021-07-29 with Mathematics categories.
A complete and definitive account of the authors' resolution of the Kervaire invariant problem in stable homotopy theory.
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 Mathematics 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.
Relational And Algebraic Methods In Computer Science
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Author : Peter Höfner
language : en
Publisher: Springer
Release Date : 2017-05-08
Relational And Algebraic Methods In Computer Science written by Peter Höfner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-08 with Mathematics categories.
This book constitutes the proceedings of the 16th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2017, held in Lyon, France, in May 2017. The 17 revised full papers and 2 invited papers presented together with 1 invited abstract were carefully selected from 28 submissions. Topics covered range from mathematical foundations to applications as conceptual and methodological tools in computer science and beyond.
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."
From Categories To Homotopy Theory
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Author : Birgit Richter
language : en
Publisher: Cambridge University Press
Release Date : 2020-04-16
From Categories To Homotopy Theory written by Birgit Richter 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 2020-04-16 with Mathematics categories.
Bridge the gap between category theory and its applications in homotopy theory with this guide for graduate students and researchers.
Homotopy Theory An Introduction To Algebraic Topology
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Author :
language : en
Publisher: Academic Press
Release Date : 1975-11-12
Homotopy Theory An Introduction To Algebraic Topology 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 1975-11-12 with Mathematics categories.
Homotopy Theory: An Introduction to Algebraic Topology