Topology And Groupoids
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Topology And Groupoids
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Author : Ronald Brown
language : en
Publisher: Booksurge Llc
Release Date : 2006
Topology And Groupoids written by Ronald Brown and has been published by Booksurge Llc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Annotation. The book is intended as a text for a two-semester course in topology and algebraic topology at the advanced undergraduate orbeginning graduate level. There are over 500 exercises, 114 figures, numerous diagrams. The general direction of the book is towardhomotopy theory with a geometric point of view. This book would providea more than adequate background for a standard algebraic topology coursethat begins with homology theory. For more information seewww.bangor.ac.uk/r.brown/topgpds.htmlThis version dated April 19, 2006, has a number of corrections made.
Topology
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Author : Ronald Brown
language : en
Publisher: Ellis Horwood
Release Date : 1988
Topology written by Ronald Brown and has been published by Ellis Horwood this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Topology categories.
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.
An Introduction To Groups Groupoids And Their Representations
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Author : Alberto Ibort
language : en
Publisher: CRC Press
Release Date : 2019-10-28
An Introduction To Groups Groupoids And Their Representations written by Alberto Ibort and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-28 with Mathematics categories.
This book offers an introduction to the theory of groupoids and their representations encompassing the standard theory of groups. Using a categorical language, developed from simple examples, the theory of finite groupoids is shown to knit neatly with that of groups and their structure as well as that of their representations is described. The book comprises numerous examples and applications, including well-known games and puzzles, databases and physics applications. Key concepts have been presented using only basic notions so that it can be used both by students and researchers interested in the subject. Category theory is the natural language that is being used to develop the theory of groupoids. However, categorical presentations of mathematical subjects tend to become highly abstract very fast and out of reach of many potential users. To avoid this, foundations of the theory, starting with simple examples, have been developed and used to study the structure of finite groups and groupoids. The appropriate language and notions from category theory have been developed for students of mathematics and theoretical physics. The book presents the theory on the same level as the ordinary and elementary theories of finite groups and their representations, and provides a unified picture of the same. The structure of the algebra of finite groupoids is analysed, along with the classical theory of characters of their representations. Unnecessary complications in the formal presentation of the subject are avoided. The book offers an introduction to the language of category theory in the concrete setting of finite sets. It also shows how this perspective provides a common ground for various problems and applications, ranging from combinatorics, the topology of graphs, structure of databases and quantum physics.
A Concise Course In Algebraic Topology
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Author : J. P. May
language : en
Publisher: University of Chicago Press
Release Date : 1999-09
A Concise Course In Algebraic Topology written by J. P. May and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09 with Mathematics categories.
Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
Foundations Of Algebraic Topology
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Author : Samuel Eilenberg
language : en
Publisher: Princeton University Press
Release Date : 2015-12-08
Foundations Of Algebraic Topology written by Samuel Eilenberg and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-08 with Mathematics categories.
The need for an axiomatic treatment of homology and cohomology theory has long been felt by topologists. Professors Eilenberg and Steenrod present here for the first time an axiomatization of the complete transition from topology to algebra. Originally published in 1952. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Groupoids In Analysis Geometry And Physics
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Author : Geometry AMS-IMS-SIAM Joint Summer Research Conference on Groupoids in Analysis
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Groupoids In Analysis Geometry And Physics written by Geometry AMS-IMS-SIAM Joint Summer Research Conference on Groupoids in Analysis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Groupoids often occur when there is symmetry of a nature not expressible in terms of groups. Other uses of groupoids can involve something of a dynamical nature. Indeed, some of the main examples come from group actions. It should also be noted that in many situations where groupoids have been used, the main emphasis has not been on symmetry or dynamics issues. For example, a foliation is an equivalence relation and has another groupoid associated with it, called the holonomy groupoid. While the implicit symmetry and dynamics are relevant, the groupoid records mostly the structure of the space of leaves and the holonomy.More generally, the use of groupoids is very much related to various notions of orbit equivalence. The point of view that groupoids describe 'singular spaces' can be found in the work of A. Grothendieck and is prevalent in the non-commutative geometry of A. Connes. This book presents the proceedings from the Joint Summer Research Conference on 'Groupoids in Analysis, Geometry, and Physics' held in Boulder, CO. The book begins with an introduction to ways in which groupoids allow a more comprehensive view of symmetry than is seen via groups. Topics range from foliations, pseudo-differential operators, $KK$-theory, amenability, Fell bundles, and index theory to quantization of Poisson manifolds. Readers will find examples of important tools for working with groupoids. This book is geared to students and researchers. It is intended to improve their understanding of groupoids and to encourage them to look further while learning about the tools used.
A Groupoid Approach To C Algebras
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Author : Jean Renault
language : en
Publisher: Springer
Release Date : 2006-11-15
A Groupoid Approach To C Algebras written by Jean Renault and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Elements Of Modern Topology
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Author : Ronald Brown
language : en
Publisher:
Release Date : 1968
Elements Of Modern Topology written by Ronald Brown and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Mathematics categories.
Groupoids Inverse Semigroups And Their Operator Algebras
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Author : Alan Paterson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Groupoids Inverse Semigroups And Their Operator Algebras written by Alan Paterson 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 2012-12-06 with Mathematics categories.
In recent years, it has become increasingly clear that there are important connections relating three concepts -- groupoids, inverse semigroups, and operator algebras. There has been a great deal of progress in this area over the last two decades, and this book gives a careful, up-to-date and reasonably extensive account of the subject matter. After an introductory first chapter, the second chapter presents a self-contained account of inverse semigroups, locally compact and r-discrete groupoids, and Lie groupoids. The section on Lie groupoids in chapter 2 contains a detailed discussion of groupoids particularly important in noncommutative geometry, including the holonomy groupoids of a foliated manifold and the tangent groupoid of a manifold. The representation theories of locally compact and r-discrete groupoids are developed in the third chapter, and it is shown that the C*-algebras of r-discrete groupoids are the covariance C*-algebras for inverse semigroup actions on locally compact Hausdorff spaces. A final chapter associates a universal r-discrete groupoid with any inverse semigroup. Six subsequent appendices treat topics related to those covered in the text. The book should appeal to a wide variety of professional mathematicians and graduate students in fields such as operator algebras, analysis on groupoids, semigroup theory, and noncommutative geometry. It will also be of interest to mathematicians interested in tilings and theoretical physicists whose focus is modeling quasicrystals with tilings. An effort has been made to make the book lucid and 'user friendly"; thus it should be accessible to any reader with a basic background in measure theory and functional analysis.