Equivariant K-Homology of the Classifying Space for Proper Actions

Mislin, Guido

doi:10.1007/978-3-0348-8089-3_1

Cited by 28 publications

(37 citation statements)

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“…In particular two models for EG are G-homotopy equivalent. For more information about the spaces EG we refer for instance to [6], [20], [26]. [32].…”

Section: Topological K -Theorymentioning

confidence: 99%

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K– andL–theory of the semi-direct product of the discrete 3–dimensional Heisenberg group by ℤ∕4

Lueck

2005

Geom. Topol.

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We compute the group homology, the topological K -theory of the reduced C * -algebra, the algebraic K -theory and the algebraic L-theory of the group ring of the semi-direct product of the three-dimensional discrete Heisenberg group by Z/4. These computations will follow from the more general treatment of a certain class of groups G which occur as extensions 1 → K → G → Q → 1 of a torsionfree group K by a group Q which satisfies certain assumptions. The key ingredients are the Baum-Connes and Farrell-Jones Conjectures and methods from equivariant algebraic topology.

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“…In particular two models for EG are G-homotopy equivalent. For more information about the spaces EG we refer for instance to [6], [20], [26]. [32].…”

Section: Topological K -Theorymentioning

confidence: 99%

“…For more information about the Baum-Connes Conjecture we refer for instance to [6], [23], [26], [33].…”

Section: Topological K -Theorymentioning

confidence: 99%

K– andL–theory of the semi-direct product of the discrete 3–dimensional Heisenberg group by ℤ∕4

Lueck

2005

Geom. Topol.

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“…A nice thorough account can be found in [18]. We say a module P in Mod F -G is projective if the functor:…”

Section: Preliminaries On Bredon Modulesmentioning

confidence: 99%

“…For a nice account concerning the universal property as well as other results on tensor products of functors see [9]. For definitions in our sense and some of the facts now to follow see [13] and [18]. Let ϕ :…”

Section: Preliminaries On Bredon Modulesmentioning

confidence: 99%

“…The definitions can easily be extended to infinite groups G and have recently regained attention through their use in equivariant obstruction theory [17] and through their connection to group actions on proper G-spaces [13,18,2,12,19]. Bredon homology also features in the Baum-Connes conjecture; a nice exposition of how the two relate can be found in [18].…”

Section: Introductionmentioning

confidence: 99%

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