Index Theory for Locally Compact Noncommutative Geometries - Couverture souple

Carey, A.L.; Gayral, V.; Rennie, A.; Sukochev, F. A.

Couverture souple

ISBN 10 : 0821898388 ISBN 13 : 9780821898383

Editeur : American Mathematical Society, 2014

Synopsis

Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, the authors prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and the authors illustrate this point with two examples in the text.

In order to understand what is new in their approach in the commutative setting the authors prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds their index formula appears to be completely new.

A propos du livre

À propos de l?auteur

A.L. Carey, Mathematical Sciences Institute, Australian National University, Canberra, Australia

V. Gayral, Universite de Reims, France

A. Rennie, University of Wollongong, Australia

F.A. Sukochev, University of New South Wales, Kensington, Australia

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2014
• Langue: anglais
• ISBN 10: 0821898388
• ISBN 13: 9780821898383
• Reliure: Broché
• Nombre de pages: 130
• Coordonnées du fabricant: Buchpark GmbH; https://www.buchpark.de; ; Krügerweg 1; Trebbin; Brandenburg; 14959; Allemagne