Computing Euler characteristics using quantum field theory

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.

13 pages, many figures; v2: final accepted manuscript with corrected typos