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- W1720160750 abstract "This paper is our first step in establishing a de Rham model for equivariant twisted $K$-theory using machinery from noncommutative geometry. Let $G$ be a compact Lie group, $M$ a compact manifold on which $G$ acts smoothly. For any $alpha in H^3_G (M, {mathbb Z})$ we introduce a notion of localized equivariant twisted cohomology $H^bullet ({bar{Omega}}^bullet (M, G, L)_g, d^alpha_{G^g})$, indexed by $gin G$. We prove that there exists a natural family of chain maps, indexed by $gin G$, inducing a family of morphisms from the equivariant periodic cyclic homology $HP^G_bullet ( C^infty (M, alpha ) )$, where $C^infty (M, alpha )$ is a certain smooth algebra constructed from an equivariant bundle gerbe defined by $alpha in H^3_G (M,{mathbb Z} )$, to $H^bullet ( {bar{Omega}}^bullet (M, G, L)_g, d^alpha_{G^g})$. We formulate a conjecture of Atiyah-Hirzebruch type theorem for equivariant twisted $K$-theory." @default.
- W1720160750 created "2016-06-24" @default.
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- W1720160750 date "2016-03-13" @default.
- W1720160750 modified "2023-10-16" @default.
- W1720160750 title "Periodic cyclic homology and equivariant gerbes" @default.
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