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Groupoids in Analysis, Geometry, and Physics

Edited by: Arlan Ramsay University of Colorado, Boulder, CO
Jean Renault Université d’Orléans, Orléans, France
Available Formats:
Electronic ISBN: 978-0-8218-7872-9
Product Code: CONM/282.E
List Price: $72.00 MAA Member Price:$64.80
AMS Member Price: $57.60 Click above image for expanded view Groupoids in Analysis, Geometry, and Physics Edited by: Arlan Ramsay University of Colorado, Boulder, CO Jean Renault Université d’Orléans, Orléans, France Available Formats:  Electronic ISBN: 978-0-8218-7872-9 Product Code: CONM/282.E  List Price:$72.00 MAA Member Price: $64.80 AMS Member Price:$57.60
• Book Details

Contemporary Mathematics
Volume: 2822001; 192 pp
MSC: Primary 22; 35; 46; 53; 57; 58;

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.

• Articles
• Alan Weinstein - Groupoids: unifying internal and external symmetry. A tour through some examples [ MR 1855239 ]
• Dana P. Williams - A primer for the Brauer group of a groupoid [ MR 1855240 ]
• Claire Anantharaman and Jean Renault - Amenable groupoids [ MR 1855241 ]
• Giulio Della Rocca and Masamichi Takesaki - The role of groupoids in classification theory: a new approach. The UHF algebra case [ MR 1855242 ]
• Paul S. Muhly - Bundles over groupoids [ MR 1855243 ]
• André Haefliger - Groupoids and foliations [ MR 1855244 ]
• Ieke Moerdijk - Étale groupoids, derived categories, and operations [ MR 1855245 ]
• Alan L. T. Paterson - The analytic index for proper, Lie groupoid actions [ MR 1855246 ]
• Pierre-Yves Le Gall - Groupoid $C^*$-algebras and operator $K$-theory [ MR 1855247 ]
• Bertrand Monthubert - Groupoids of manifolds with corners and index theory [ MR 1855248 ]
• N. P. Landsman and B. Ramazan - Quantization of Poisson algebras associated to Lie algebroids [ MR 1855249 ]
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 2822001; 192 pp
MSC: Primary 22; 35; 46; 53; 57; 58;

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.

• Articles
• Alan Weinstein - Groupoids: unifying internal and external symmetry. A tour through some examples [ MR 1855239 ]
• Dana P. Williams - A primer for the Brauer group of a groupoid [ MR 1855240 ]
• Claire Anantharaman and Jean Renault - Amenable groupoids [ MR 1855241 ]
• Giulio Della Rocca and Masamichi Takesaki - The role of groupoids in classification theory: a new approach. The UHF algebra case [ MR 1855242 ]
• Paul S. Muhly - Bundles over groupoids [ MR 1855243 ]
• André Haefliger - Groupoids and foliations [ MR 1855244 ]
• Ieke Moerdijk - Étale groupoids, derived categories, and operations [ MR 1855245 ]
• Alan L. T. Paterson - The analytic index for proper, Lie groupoid actions [ MR 1855246 ]
• Pierre-Yves Le Gall - Groupoid $C^*$-algebras and operator $K$-theory [ MR 1855247 ]
• Bertrand Monthubert - Groupoids of manifolds with corners and index theory [ MR 1855248 ]
• N. P. Landsman and B. Ramazan - Quantization of Poisson algebras associated to Lie algebroids [ MR 1855249 ]
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.