Equivariant KK-theory and noncommutative index theory
نویسنده
چکیده
منابع مشابه
Duality, Correspondences and the Lefschetz Map in Equivariant Kk-theory: a Survey
We survey work by the author and Ralf Meyer on equivariant KKtheory. Duality plays a key role in our approach. We organize the survey around the objective of computing a certain homotopy-invariant of a space equipped with a proper action of a group or groupoid called the Lefschetz map. The latter associates an equivariant K-homology class to an equivariant Kasparov self-morphism of a space X ad...
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For equivariant stable homotopy theory, equivariant KK-theory and equivariant derived categories, we show how restriction to a subgroup of finite index yields a finite commutative separable extension, analogous to finite étale extensions in algebraic geometry.
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Let G be a locally compact, σ-compact group. We prove that the equivariant KK-theory, KK, is the universal category for functors from G-algebras to abelian groups which are stable, homotopy invariant and split-exact. This is a generalization of Higsons characterisation of (non-equivariant) KK-theory.
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We present the review of noncommutative symmetries applied to Connes’ formulation of spectral triples. We introduce the notion of equivariant spectral triples with Hopf algebras as isometries of noncommutative manifolds, relate it to other elements of theory (equivariant K-theory, homology, equivariant differential algebras) and provide several examples of spectral triples with their isometries...
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A. The aim of this talk and the next is to explain two important aspects of equivariant Kasparov theory, especially for smooth manifolds: duality, and the topological description of equivariant KK-groups using equivariant correspondences. In the first talk we will review the basic definitions of KK-theory, including the Thom isomorphism. We then explain duality, which gives a way of redu...
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