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.
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Acknowledgments
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.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Pflaum, M.J., Posthuma, H. & Tang, X. On the Algebraic Index for Riemannian Étale Groupoids. Lett Math Phys 90, 287–310 (2009). https://doi.org/10.1007/s11005-009-0339-y
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DOI: https://doi.org/10.1007/s11005-009-0339-y