Coarse flow spaces for relatively hyperbolic groups

Abstract

We introduce a coarse flow space for relatively hyperbolic groups and use it 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).

Final version, to appear in Compositio

References in corpus (1)

• The K-theoretic Farrell-Jones Conjecture for hyperbolic groups

Cited by in corpus (9)

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• Warped cones, (non-)rigidity, and piecewise properties, with a joint appendix with Dawid Kielak
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• Dynamic asymptotic dimension for actions of virtually cyclic groups
• Injectivity results for coarse homology theories
• Helly groups, coarsely Helly groups, and relative hyperbolicity
• Nuclear dimension of subhomogeneous twisted groupoid C*-algebras and dynamic asymptotic dimension
• Farrell-Jones via Dehn fillings