hal-00474026, version 1

The $K$-groups and the index theory of certain comparison $C^*$-algebras

Bertrand Monthubert () ¹, Victor Nistor () ²

Noncommutative Geometric Methods in Global Analysis (2009)

• 1:  Institut de Mathématiques de Toulouse (IMT)
• 
  Université Paul Sabatier [UPS] - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées (INSA) - Toulouse – CNRS : UMR5219 Bâtiment 1R3 118 route de Narbonne 31062 TOULOUSE CEDEX 4 France
• 2:  Departement of Mathematics
• www.math.psu.edu
  The Pennsylvania State University United States

Bibliographic reference

• Type of document: Invited conferences
• Subject:

  Mathematics/K-Theory and Homology

  Mathematics/Operator Algebras

• Title: The $K$-groups and the index theory of certain comparison $C^*$-algebras
• Abstract: We compute the $K$-theory of comparison $C^*$-algebra associated to a manifold with corners. These comparison algebras are an example of the abstract pseudodifferential algebras introduced by Connes and Moscovici \cite{M3}. Our calculation is obtained by showing that the comparison algebras are a homomorphic image of a groupoid $C^*$-algebra. We then prove an index theorem with values in the $K$-theory groups of the comparison algebra.
• Fulltext language: English
• Production date: 2010-04-18
• Audience: international
• Conference or book title: Noncommutative Geometric Methods in Global Analysis
• Conference date: 2009-06-29
• Conference date (end): 2009-07-04
• City: Bonn
• Country: Germany
• Keyword(s): Comparison algebra – Index theory – Manifolds with corners
• Classification: 58J20;58J40;19M05

Attached file list to this document: 

• hal-00474026, version 1
• http://hal.archives-ouvertes.fr/hal-00474026
• oai:hal.archives-ouvertes.fr:hal-00474026
• From: Bertrand Monthubert <>
• Submitted on: Sunday, 18 April 2010 17:37:24
• Updated on: Monday, 19 April 2010 08:47:10