KK-theoretic duality for proper twisted actions |
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Authors: | Siegfried Echterhoff Heath Emerson Hyun Jeong Kim |
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Institution: | 1. Mathematisches Institut, Westf?lische Wilhelms-Universit?t Münster, Einsteinstr. 62, 48149, Münster, Germany 2. Department of Mathematics and Statistics, University of Victoria, P.O. Box 3045, STN CSC, Victoria, BC, Canada
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Abstract: | Let be a smooth continuous trace algebra, with a Riemannian manifold spectrum X, equipped with a smooth action by a discrete group G such that G acts on X properly and isometrically. Then is KK-theoretically Poincaré dual to , where is the inverse of in the Brauer group of Morita equivalence classes of continuous trace algebras equipped with a group action. We deduce this
from a strengthening of Kasparov’s duality theorem. As applications we obtain a version of the above Poincaré duality with
X replaced by a compact G-manifold M and Poincaré dualities for twisted group algebras if the group satisfies some additional properties related to the Dirac
dual-Dirac method for the Baum- Connes conjecture.
This research was supported by the EU-Network Quantum Spaces and Noncommutative Geometry (Contract HPRN-CT-2002-00280) and the Deutsche Forschungsgemeinschaft (SFB 478) and by the National Science and Engineering Research Council of Canada Discovery Grant program. |
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Keywords: | 19K35 46L80 |
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