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Nonabelian Algebraic Topology = Filt...

Brown, Ronald,

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Nonabelian Algebraic Topology = Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Nonabelian Algebraic Topology/ Ronald Brown, Philip J. Higgins, Rafael Sivera
Reminder of title:	Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids /
Author:	Brown, Ronald,
other author:	Higgins, Philip J.,
Published:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2011,
Description:	1 online resource (703 pages)
Subject:	Algebraic topology - Congresses. -
Online resource:	https://doi.org/10.4171/083
Online resource:	https://www.ems-ph.org/img/books/brown_mini.jpg
ISBN:	9783037195833

Nonabelian Algebraic Topology = Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids /
Brown, Ronald,

Nonabelian Algebraic TopologyFiltered Spaces, Crossed Complexes, Cubical Homotopy Groupoids /[electronic resource] :Ronald Brown, Philip J. Higgins, Rafael Sivera - Zuerich, Switzerland :European Mathematical Society Publishing House,2011 - 1 online resource (703 pages) - EMS Tracts in Mathematics (ETM)15.

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

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 ω-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.

ISBN: 9783037195833

Standard No.: 10.4171/083doiSubjects--Topical Terms:

1575359
Algebraic topology
--Congresses.

Nonabelian Algebraic Topology = Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids /
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520 $a 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 ω-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.
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