On the Algebraic Index for Riemannian Étale Groupoids

  • Markus J. Pflaum
  • Hessel Posthuma
  • Xiang Tang
Open Access


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 


Riemannian foliation deformation quantization index cyclic cohomology 



X. Tang’s research is partially supported by NSF Grant 0703775. H. Posthuma acknowledges support by NWO. M. Pflaum and H. Posthuma thank the Department of Mathematics of Washington University, St. Louis, MO, for hosting a research visit.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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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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