Coarse flow spaces for relatively hyperbolic groups

TL;DR

This paper introduces a new coarse flow space for relatively hyperbolic groups, enabling the reduction of the Farrell-Jones Conjecture to peripheral subgroups, thus advancing understanding of their algebraic K- and L-theory.

Contribution

It develops a coarse flow space framework for relatively hyperbolic groups and applies it to verify boundary action regularity, linking group properties to algebraic conjectures.

Findings

Verified regularity condition for boundary actions

Reduced Farrell-Jones Conjecture to peripheral subgroups

Provided new tools for studying 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).