Letters in Mathematical Physics

, 90:287

On the Algebraic Index for Riemannian Étale Groupoids

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Abstract

In this paper, we construct an explicit quasi-isomorphism to study the cyclic cohomology of a deformation quantization over a Riemannian étale groupoid. Such a quasi-isomorphism allows us to propose a general algebraic index problem for Riemannian étale groupoids. We discuss solutions to that index problem when the groupoid is proper or defined by a constant Dirac structure on a 3-dimensional torus.

Mathematics Subject Classification (2000)

Primary 58J20 Secondary 53D55 

Keywords

Riemannian foliation deformation quantization index cyclic cohomology 

Copyright information

© The Author(s) 2009

Authors and Affiliations

  • Markus J. Pflaum
    • 1
  • Hessel Posthuma
    • 2
  • Xiang Tang
    • 3
  1. 1.Department of MathematicsUniversity of ColoradoBoulderUSA
  2. 2.Korteweg-de Vries Institute for MathematicsUniversity of AmsterdamAmsterdamThe Netherlands
  3. 3.Department of MathematicsWashington UniversitySt. LouisUSA

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