Equivariant Poincaré duality for quantum group actions.

Ryszard Nest; Christian Voigt

Equivariant Poincaré duality for quantum group actions.

Department of Mathematical Sciences

23 Citations (Scopus)

Abstract

We extend the notion of Poincaré 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 Podleś sphere is equivariantly Poincaré dual to itself.

Original language	English
Journal	Journal of Functional Analysis
Volume	258
Issue number	5
Pages (from-to)	1466-1503
Number of pages	37
ISSN	0022-1236
Publication status	Published - 1 Mar 2010

Cite this

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abstract = "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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AB - We extend the notion of Poincaré 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 Podleś sphere is equivariantly Poincaré dual to itself.

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EP - 1503

JO - Journal of Functional Analysis

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Equivariant Poincaré duality for quantum group actions.

Abstract

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