topology and groupoids

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Topology And Groupoids

Author : Ronald Brown
ISBN : 1419627228
Genre : Mathematics
File Size : 33. 30 MB
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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 version dated April 19, 2006, has a number of corrections made.

Nonabelian Algebraic Topology

Author : Ronald Brown
ISBN : 3037190833
Genre : Mathematics
File Size : 38. 23 MB
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Groupoids Inverse Semigroups And Their Operator Algebras

Author : Alan Paterson
ISBN : 9781461217749
Genre : Mathematics
File Size : 89. 93 MB
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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.

Topology Via Logic

Author : Steven Vickers
ISBN : 0521576512
Genre : Computers
File Size : 40. 75 MB
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This is an advanced textbook on topology for computer scientists. It is based on a course given by the author to postgraduate students of computer science at Imperial College.

Introduction To Foliations And Lie Groupoids

Author : I. Moerdijk
ISBN : 1139438980
Genre : Mathematics
File Size : 85. 52 MB
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This book gives a quick introduction to the theory of foliations, Lie groupoids and Lie algebroids. An important feature is the emphasis on the interplay between these concepts: Lie groupoids form an indispensable tool to study the transverse structure of foliations as well as their noncommutative geometry, while the theory of foliations has immediate applications to the Lie theory of groupoids and their infinitesimal algebroids. The book starts with a detailed presentation of the main classical theorems in the theory of foliations then proceeds to Molino's theory, Lie groupoids, constructing the holonomy groupoid of a foliation and finally Lie algebroids. Among other things, the authors discuss to what extent Lie's theory for Lie groups and Lie algebras holds in the more general context of groupoids and algebroids. Based on the authors' extensive teaching experience, this book contains numerous examples and exercises making it ideal for graduate students and their instructors.

Graph Groupoids And Their Topology

Author : Adrian Wilson
ISBN : OCLC:179884282
Genre :
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The dissertation investigates graph groupoids and the path spaces associated with their unit spaces. It was shown by Paterson and Welch that for a general directed graph [varepsilon], the path space X = Y [union] Z, where Y is the set of finite paths and Z the set of infinite paths in [varepsilon], is a locally compact metric space. The dissertation solves three main questions. For the first, a natural question that was asked by A. Kumjian (University of Nevada at Reno) in the case of the Cuntz graph [varepsilon] [infinity] was how the topological space X relates to an earlier topological space investigated by J. Renault (Orleans). I show that the two topological spaces are homeomorphic and so can be identified. The dissertation then discusses the graph groupoid for [varepsilon] in the general case. For this investigation, it is important to be able to use the axiomatic approach to groupoids, and I show that this is equivalent to the usual definition of a groupoid as a "small category with inverses". This proof of this equivalence answers the second main question answered by the dissertation. The third main question is to construct the graph groupoid G [varepsilon] for [varepsilon] and prove that it is a second countable, locally compact, Hausdorff groupoid. The construction and proof of this are given in the last section of the dissertation. (The proof of the corresponding result for row finite graphs had been sketched earlier in the work of, e.g., Kumjian, Raeburn and Renault.).


Author : Ronald Brown
ISBN : UOM:39015042078504
Genre : Mathematics
File Size : 23. 27 MB
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How Surfaces Intersect In Space

Author : J. Scott Carter
ISBN : 9810220669
Genre : Science
File Size : 45. 72 MB
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This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. It will be of value to anyone who wants to understand the subject by way of examples. Undergraduates, beginning graduate students, and non-professionals will profit from reading the book and from just looking at the pictures.

A Concise Course In Algebraic Topology

Author : J. P. May
ISBN : 0226511839
Genre : Mathematics
File Size : 58. 31 MB
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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.

Algebraic Topology

Author : Nils Baas
ISBN : 9783642012006
Genre : Mathematics
File Size : 86. 84 MB
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The 2007 Abel Symposium took place at the University of Oslo in August 2007. The goal of the symposium was to bring together mathematicians whose research efforts have led to recent advances in algebraic geometry, algebraic K-theory, algebraic topology, and mathematical physics. A common theme of this symposium was the development of new perspectives and new constructions with a categorical flavor. As the lectures at the symposium and the papers of this volume demonstrate, these perspectives and constructions have enabled a broadening of vistas, a synergy between once-differentiated subjects, and solutions to mathematical problems both old and new.

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