Equivariant Poincaré duality for quantum group actions

Details Equivariant Poincaré duality for quantum group actions Equivariant Poincaré duality for quantum group actions

2009-02-23

arxiv.org/abs/0902.3987v2

Mathematics

K-Theory and Homology

Minor changes. To appear in J. Funct. Anal

Scientific paper

We extend the notion of Poincar\'e duality in KK-theory to the setting of quantum group actions. An important ingredient in our approach is the replacement of ordinary tensor products by braided tensor products. Along the way we discuss general properties of equivariant KK-theory for locally compact quantum groups, including the construction of exterior products. As an example, we prove that the standard Podle\'s sphere is equivariantly Poincar\'e dual to itself.

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