Asymptotic homology of graph braid groups

TL;DR

This paper provides explicit formulas for the asymptotic Betti numbers of unordered configuration spaces on finite graphs, advancing understanding of their topological properties over various fields.

Contribution

It introduces a general method to compute asymptotic Betti numbers for configuration spaces on any finite graph, regardless of the field.

Findings

Explicit formulas for asymptotic Betti numbers

Applicable to any finite graph and field

Enhances understanding of graph configuration space topology

Abstract

We give explicit formulas for the asymptotic Betti numbers of the unordered configuration spaces of an arbitrary finite graph over an arbitrary field.