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Coarse flow spaces for relatively hyperbolic groups

Part of: Categories and geometry $K$-theory of forms Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 March 2017

A. Bartels
A. Bartels*
Affiliation:
Westfälische Wilhelms-Universität Münster, Mathematisches Institut, Einsteinstr. 62, D-48149 Münster, Germany email a.bartels@wwu.de
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Abstract

We introduce coarse flow spaces for relatively hyperbolic groups and use them to verify a regularity condition for the action of relatively hyperbolic groups on their boundaries. As an application the Farrell–Jones conjecture for relatively hyperbolic groups can be reduced to the peripheral subgroups (up to index-2 overgroups in the $L$-theory case).

Keywords

Farrell–Jones conjectureK- and L-theory of group rings

MSC classification

Primary: 18F25: Algebraic $K$-theory and $L$-theory 19G24: $L$-theory of group rings 20F67: Hyperbolic groups and nonpositively curved groups
Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 4 , April 2017 , pp. 745 - 779
Copyright
© The Author 2017 

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