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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 28 (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.
Induction theorems and isomorphism conjectures for K and Ltheory
 PREPRINTREIHE SFB 478 — 38 STRUKTUREN IN DER MATHEMATIK, HEFT 331
, 2004
"... The FarrellJones and the BaumConnes Conjecture say that one can compute the algebraic K and Ltheory of the group ring and the topological Ktheory of the reduced group C∗algebra of a group G in terms of these functors for the virtually cyclic subgroups or the finite subgroups of G. By induction ..."
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Cited by 12 (9 self)
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The FarrellJones and the BaumConnes Conjecture say that one can compute the algebraic K and Ltheory of the group ring and the topological Ktheory of the reduced group C∗algebra of a group G in terms of these functors for the virtually cyclic subgroups or the finite subgroups of G. By induction theory we want to reduce these families of subgroups to a smaller family, for instance to the family of subgroups which are either finite hyperelementary or extensions of finite hyperelementary groups with Z as kernel or to the family of finite cyclic subgroups. Roughly speaking, we extend the induction theorems of Dress for finite groups to infinite groups.
ON THE KTHEORY OF GROUPS WITH FINITE ASYMPTOTIC DIMENSION
"... Abstract. It is proved that the assembly maps in algebraic K and Ltheory with respect to the family of finite subgroups is injective for groups Γ with finite asymptotic dimension that admit a finite model for EΓ. The result also applies to certain groups that admit only a finite dimensional model ..."
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Cited by 6 (2 self)
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Abstract. It is proved that the assembly maps in algebraic K and Ltheory with respect to the family of finite subgroups is injective for groups Γ with finite asymptotic dimension that admit a finite model for EΓ. The result also applies to certain groups that admit only a finite dimensional model for EΓ. In particular, it applies to discrete subgroups of virtually connected Lie groups.
Buildings and their applications in geometry and topology
 ASIAN J. MATH
"... Buildings were first introduced by J.Tits in 1950s to give systematic geometric interpretations of exceptional Lie groups and have been generalized in various ways: Euclidean buildings (BruhatTits buildings), topological buildings, Rbuildings, in particular Rtrees. They are useful for many differ ..."
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Cited by 4 (2 self)
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Buildings were first introduced by J.Tits in 1950s to give systematic geometric interpretations of exceptional Lie groups and have been generalized in various ways: Euclidean buildings (BruhatTits buildings), topological buildings, Rbuildings, in particular Rtrees. They are useful for many different applications in various subjects: algebraic groups, finite groups, finite geometry, representation theory over local fields, algebraic geometry, Arakelov intersection for arithmetic varieties, algebraic Ktheories, combinatorial group theory, global geometry and algebraic topology, in particular cohomology groups, of arithmetic groups and Sarithmetic groups, rigidity of cofinite subgroups of semisimple Lie groups and nonpositively curved manifolds, classification of isoparametric submanifolds in R n of high codimension, existence of hyperbolic structures on three dimensional manifolds in Thurston’s geometrization program. In this paper, we survey several applications of buildings in differential geometry and geometric topology. There are four underlying themes in these applications: 1. Buildings often describe the geometry at infinity of symmetric spaces and locally symmetric
CONTINUOUS CONTROL AND THE ALGEBRAIC LTHEORY ASSEMBLY MAP
, 2003
"... Abstract. In this work, the assembly map in Ltheory for the family of finite subgroups is proven to be a split injection for a class of groups. Groups in this class, including virtually polycyclic groups, have universal spaces that satisfy certain geometric conditions. The proof follows the method ..."
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Cited by 2 (2 self)
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Abstract. In this work, the assembly map in Ltheory for the family of finite subgroups is proven to be a split injection for a class of groups. Groups in this class, including virtually polycyclic groups, have universal spaces that satisfy certain geometric conditions. The proof follows the method developed by CarlssonPedersen to split the assembly map in the case of torsion free groups. Here, the continuously controlled techniques and results are extended to handle groups with torsion. 1.
ASSEMBLY MAPS FOR GROUP EXTENSIONS IN KTHEORY AND LTHEORY WITH TWISTED COEFFICIENTS
"... Abstract. In this paper we show that the FarrellJones isomorphism conjectures are inherited in group extensions for assembly maps in Ktheory and Ltheory with twisted coefficients. ..."
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Abstract. In this paper we show that the FarrellJones isomorphism conjectures are inherited in group extensions for assembly maps in Ktheory and Ltheory with twisted coefficients.
SPLIT INJECTIVITY OF THE BAUMCONNES ASSEMBLY MAP
, 2003
"... Abstract. In this work, the continuously controlled techniques developed by Carlsson and Pedersen are used to prove that the BaumConnes map is a split injection for groups satisfying certain geometric conditions. 1. ..."
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Abstract. In this work, the continuously controlled techniques developed by Carlsson and Pedersen are used to prove that the BaumConnes map is a split injection for groups satisfying certain geometric conditions. 1.
SURVEY ON GEOMETRIC GROUP THEORY
, 806
"... Abstract. This article is a survey article on geometric group theory from the point of view of a nonexpert who likes geometric group theory and uses it in his own research. This survey article on geometric group theory is written by a nonexpert who likes geometric group theory and uses it in his o ..."
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Abstract. This article is a survey article on geometric group theory from the point of view of a nonexpert who likes geometric group theory and uses it in his own research. This survey article on geometric group theory is written by a nonexpert who likes geometric group theory and uses it in his own research. It is meant as a service for people who want to receive an impression and read an introduction about the topic and possibly will later pass to more elaborate and specialized survey articles