Roe functors preserve homotopies

TL;DR

This paper demonstrates that coarse maps induce natural transformations of certain endofunctors on C*-algebras and that this relationship remains invariant under coarse homotopies, linking coarse geometry with operator algebras.

Contribution

It establishes a new connection between coarse geometry and C*-algebra functors, showing invariance under coarse homotopies.

Findings

Coarse maps induce natural transformations of endofunctors on C*-algebras.

The correspondence is invariant under coarse homotopies.

Bridges coarse geometric concepts with operator algebra theory.

Abstract

We show that coarse maps between countable metric spaces of bounded geometry induce natural transformations of sufficiently good endofunctors of C*-algebras and prove that this correspondence is invariant with respect to coarse homotopies.