Computing Euler characteristics using quantum field theory

TL;DR

This paper introduces a novel approach using quantum field theory to compute the virtual Euler characteristics of automorphism groups of free groups and related graph complexes, aiding asymptotic analysis.

Contribution

It develops a method applying quantum field theory techniques to derive power series encoding Euler characteristics, advancing computational tools in algebraic topology.

Findings

Derived formal power series for Euler characteristics

Connected quantum field theory methods to topological invariants

Facilitated asymptotic analysis of $ ext{Out}(F_n)$

Abstract

This paper explains how to use quantum field theory techniques to find formal power series that encode the virtual Euler characteristics of $\mathrm{Out}(F_n)$ and related graph complexes. Finding such power series was a necessary step in the asymptotic analysis of $\chi(\mathrm{Out}(F_n))$ carried out in the authors' previous paper.