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Groupoids in Analysis, Geometry, and Physics
Edited by: Arlan Ramsay, University of Colorado, Boulder, CO, and Jean Renault, Université d'Orléans, France

Contemporary Mathematics
2001; 192 pp; softcover
Volume: 282
ISBN-10: 0-8218-2042-7
ISBN-13: 978-0-8218-2042-1
List Price: US$68
Member Price: US$54.40
Order Code: CONM/282
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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.


Graduate students and research mathematicians interested in differential geometry, operator algebras, index theory, quantization of classical systems and related mathematics.

Table of Contents

  • A. Weinstein -- Groupoids: Unifying internal and external symmetry-A tour through some examples
  • D. P. Williams -- A primer for the Brauer group of a groupoid
  • C. Anantharaman and J. Renault -- Amenable groupoids
  • G. Della Rocca and M. Takesaki -- The role of groupoids in classification theory. A new approach. The UHF algebra case
  • P. S. Muhly -- Bundles over groupoids
  • A. Haefliger -- Groupoids and foliations
  • I. Moerdijk -- Etale groupoids, derived categories, and operations
  • A. L. T. Paterson -- The analytic index for proper, Lie groupoid actions
  • P.-Y. Le Gall -- Groupoid \(C^*\)-algebras and operator \(K\)-theory
  • B. Monthubert -- Groupoids of manifolds with corners and index theory
  • N. P. Landsman and B. Ramazan -- Quantization of Poisson algebras associated to Lie algebroids
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