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165
The type of the classifying space for a family of subgroups
 J. Pure Appl. Algebra
"... We define for a topological group G and a family of subgroupsF two versions for the classifying space for the family F, the GCWversion EF(G) and the numerable Gspace version JF(G). They agree if G is discrete, or if G is a Lie group and each element inF compact, or ifF is the family of compact su ..."
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Cited by 108 (31 self)
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We define for a topological group G and a family of subgroupsF two versions for the classifying space for the family F, the GCWversion EF(G) and the numerable Gspace version JF(G). They agree if G is discrete, or if G is a Lie group and each element inF compact, or ifF is the family of compact subgroups. We discuss special geometric models for these spaces for the family of compact open groups in special cases such as almost connected groups G and word hyperbolic groups G. We deal with the question whether there are finite models, models of finite type, finite dimensional models. We also discuss the relevance of these spaces for the BaumConnes Conjecture about the topological Ktheory of the reduced group C ∗algebra, for the FarrellJones Conjecture about the algebraic Kand Ltheory of group rings, for Completion Theorems and for classifying spaces for equivariant vector bundles and for other situations.
Spaces over a category and assembly maps in isomorphism conjectures
 in K  and Ltheory, K Theory 15
, 1998
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Coefficients for the FarrellJones conjecture
 Preprintreihe SFB 478 — Geometrische Strukturen in der Mathematik, Heft 402
"... Abstract. We introduce the FarrellJones Conjecture with coefficients in an additive category with Gaction. This is a variant of the FarrellJones Conjecture about the algebraic K or LTheory of a group ring RG. It allows to treat twisted group rings and crossed product rings. The conjecture with ..."
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Cited by 54 (12 self)
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Abstract. We introduce the FarrellJones Conjecture with coefficients in an additive category with Gaction. This is a variant of the FarrellJones Conjecture about the algebraic K or LTheory of a group ring RG. It allows to treat twisted group rings and crossed product rings. The conjecture with coefficients is stronger than the original conjecture but it has better inheritance properties. Since known proofs using controlled algebra carry over to the setup with coefficients we obtain new results about the original FarrellJones Conjecture. The conjecture with coefficients implies the fibered version of the FarrellJones Conjecture. 1.
The BaumConnes and the FarrellJones conjectures in K and Ltheory
 Preprintreihe SFB 478 — Geometrische Strukturen in der Mathematik, Heft 324
, 2004
"... Summary. We give a survey of the meaning, status and applications of the BaumConnes Conjecture about the topological Ktheory of the reduced group C ∗algebra and the FarrellJones Conjecture about the algebraic K and Ltheory of the group ring of a (discrete) group G. Key words: K and Lgroups o ..."
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Cited by 53 (26 self)
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Summary. We give a survey of the meaning, status and applications of the BaumConnes Conjecture about the topological Ktheory of the reduced group C ∗algebra and the FarrellJones Conjecture about the algebraic K and Ltheory of the group ring of a (discrete) group G. Key words: K and Lgroups of group rings and group C ∗algebras, BaumConnes
The Borel conjecture for hyperbolic and CAT(0)groups
 ANN. OF MATH
, 2009
"... We prove the Borel Conjecture for a class of groups containing wordhyperbolic groups and groups acting properly, isometrically and cocompactly on a finite dimensional CAT(0)space. ..."
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Cited by 50 (12 self)
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We prove the Borel Conjecture for a class of groups containing wordhyperbolic groups and groups acting properly, isometrically and cocompactly on a finite dimensional CAT(0)space.
The Ktheoretic FarrellJones Conjecture for hyperbolic groups
 Invent. Math
"... Abstract. We prove the Ktheoretic FarrellJones Conjecture for hyperbolic groups with (twisted) coefficients in any associative ring with unit. ..."
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Cited by 41 (18 self)
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Abstract. We prove the Ktheoretic FarrellJones Conjecture for hyperbolic groups with (twisted) coefficients in any associative ring with unit.
Isomorphism conjecture for homotopy Ktheory and groups acting on trees
, 2008
"... We discuss an analogon to the FarrellJones Conjecture for homotopy algebraic Ktheory. In particular, we prove that if a group G acts on a tree and all isotropy groups satisfy this conjecture, then G satisfies this conjecture. This result can be used to get rational injectivity results for the asse ..."
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Cited by 41 (13 self)
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We discuss an analogon to the FarrellJones Conjecture for homotopy algebraic Ktheory. In particular, we prove that if a group G acts on a tree and all isotropy groups satisfy this conjecture, then G satisfies this conjecture. This result can be used to get rational injectivity results for the assembly map in the FarrellJones Conjecture in algebraic Ktheory.
Periodic complexes and group actions
, 2001
"... In this paper we show that the cohomology of a connected CW–complex is periodic if and only if it is the base space of a spherical fibration with total space that is homotopically finite dimensional. As applications we characterize those discrete groups that act freely and properly on R n × S m; we ..."
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Cited by 29 (0 self)
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In this paper we show that the cohomology of a connected CW–complex is periodic if and only if it is the base space of a spherical fibration with total space that is homotopically finite dimensional. As applications we characterize those discrete groups that act freely and properly on R n × S m; we construct non–standard free actions of rank two simple groups on finite complexes Y ≃ S n × S m; and we prove that a finite p–group P acts freely on such a complex if and only if it does not contain a subgroup isomorphic to (Z/p)³.
THE FARRELLJONES CONJECTURE FOR COCOMPACT LATTICES IN VIRTUALLY CONNECTED LIE GROUPS
, 2013
"... Let G be a cocompact lattice in a virtually connected Lie group or the fundamental group of a 3dimensional manifold. We prove the K and Ltheoretic FarrellJones Conjecture for G. ..."
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Cited by 25 (4 self)
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Let G be a cocompact lattice in a virtually connected Lie group or the fundamental group of a 3dimensional manifold. We prove the K and Ltheoretic FarrellJones Conjecture for G.