# Coarse assembly maps

## TL;DR

This paper constructs a general coarse assembly map for strong coarse homology theories, providing conditions for it to be an equivalence and explicitly calculating its domain, thus generalizing known results in coarse geometry.

## Contribution

It introduces a universal construction of coarse assembly maps for broad classes of coarse homology theories and extends known equivalence results.

## Key findings

- Conditions under which the assembly map is an equivalence
- Explicit calculation of the domain of the assembly map
- Generalization of analytic coarse assembly map results

## Abstract

For every strong coarse homology theory we construct a coarse assembly map as a natural transformation between coarse homology theories. We provide various conditions implying that this assembly map is an equivalence. These results generalize known results for the analytic coarse assembly map for K-homology to general coarse homology theories. Furthermore, we calculate the domain of the coarse assembly map explicitly in terms of locally finite homology theory.