Long and thin covers for flow spaces

TL;DR

This paper introduces a new, more general method for constructing long and thin covers of flow spaces, which are crucial in proving the Farrell--Jones conjecture for various groups, simplifying existing arguments.

Contribution

It provides an alternative, simplified construction of flow space covers applicable in broader contexts than previous methods.

Findings

New construction of flow space covers that is more general

Simplification of arguments in Farrell--Jones conjecture proofs

Applicable to hyperbolic and CAT(0)-groups

Abstract

Long and thin covers of flow spaces are important ingredients in the proof of the Farrell--Jones conjecture for certain classes of groups, like hyperbolic and CAT(0)-groups. In this paper we provide an alternative construction of such covers which holds in a more general setting and simplifies some of the arguments.