The K-theory of Twisted Group Algebras

Echterhoff, Siegfried

doi:10.1007/978-3-7643-8604-7_3

Cited by 7 publications

(7 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The map t → U (t) is a twisted left-regular representation of R p on L 2 (R p ), in the sense of [36].…”

Section: Definitions For Noncommutativementioning

confidence: 99%

The Connes character formula for locally compact spectral triples

Sukochev,

Zanin

2018

Preprint

View full text Add to dashboard Cite

show abstract

“…The map t → U (t) is a twisted left-regular representation of R p on L 2 (R p ), in the sense of [36].…”

Section: Definitions For Noncommutativementioning

confidence: 99%

The Connes character formula for locally compact spectral triples

Sukochev,

Zanin

2018

Preprint

View full text Add to dashboard Cite

show abstract

“…and A Ì G denotes the crossed product C -algebra. See Chabert and Echterhoff [7] and Echterhoff [11] for more details.…”

Section: Theorem 62mentioning

confidence: 99%

“…Related duality isomorphisms have been deduced for almost connected groups by Echterhoff [11] using methods from equivariant Kasparov KK-theory (particularly the Dirac-dual Dirac method) and positive results for the Baum-Connes conjecture with coefficients [12].…”

Section: Theorem 62mentioning

confidence: 99%

Twisted equivariant

Bárcenas

Velásquez

2014

Algebr. Geom. Topol.

View full text Add to dashboard Cite

We use a spectral sequence to compute twisted equivariant K-theory groups for the classifying space of proper actions of discrete groups. We study a form of Poincaré duality for twisted equivariant K-theory studied by Echterhoff, Emerson and Kim in the context of the Baum-Connes conjecture with coefficients and verify it for the group Sl 3 .Z/. 19L47; 55N91, 46L80 In this work, we examine computational aspects relevant to the computation of twisted equivariant K-theory and K-homology groups for proper actions of discrete groups. Twisted K-theory was introduced by Donovan and Karoubi [9] assigning to a torsion element˛2 H 3 .X; Z/ an abelian group˛K .X / defined on a space by using finitedimensional matrix bundles. After the growing interest by physicists in the 1990s and 2000s, Atiyah and Segal [2] introduced a notion of twisted equivariant K-theory for actions of compact Lie groups. In another direction, orbifold versions of twisted K-theory were introduced by Adem and Ruan [1], and progress was made to develop computational tools for twisted equivariant K-theory with the construction of a spectral sequence by the authors, Espinoza and Uribe in [5]. In [4], the first author, Espinoza, Joachim and Uribe introduce twisted equivariant K-theory for proper actions, allowing a more general class of twists, classified by the third integral Borel cohomology group H 3 .X G EG; Z/.

show abstract

“…However, the definition of such an invariant has been only given in particular cases [11], [13] using Kasparov KK-Theory and rather ad-hoc methods inspired in ideas related the solution of the Connes-Kasparov conjecture by Chabert, Echterhoff and Nest [12].…”

Section: Introductionmentioning

confidence: 99%

“…Date: October 20, 2018. In section 4, the construction is compared to equivariant Kasparov KK-groups via the definition of an index map, which is proved in Theorem 4.6 to give an isomorphism between both constructions in the case of a proper, finite G-CW complex. On the way, several results, including versions of KK-Theoretical Poincaré Duality [14], [13] and consequences of the Thom isomorphisms and Pushforward Maps for Twisted Equivariant K-Theory of [3] are discussed.…”

Section: Introductionmentioning

confidence: 99%