The Bounded Isomorphism Conjecture for Spaces of Graphs with Large Girth

TL;DR

This paper proves a coarse version of the Farrell-Jones conjecture for spaces of graphs with large girth, extending techniques from hyperbolic groups to new classes of geometric spaces.

Contribution

It introduces and verifies the bounded isomorphism conjecture for graphs with large girth using adapted techniques from hyperbolic group theory.

Findings

Verifies the bounded isomorphism conjecture for large girth graphs

Extends methods from hyperbolic groups to graph spaces

Provides new insights into coarse geometric properties

Abstract

In this article we study a coarse version of the K-theoretic Farrell-Jones conjecture we call coarse or bounded isomorphism conjecture. With techniques that have already been used to prove the Farrell-Jones conjecture for hyperbolic groups we are able to verify the bounded isomorphism conjecture for spaces of graphs with large girth and bounded geometry.