The rational homology of the outer automorphism group of $F_7$

TL;DR

This paper computes the rational homology groups of the outer automorphism group of a free group of rank 7, revealing new homology classes beyond previously known types.

Contribution

It provides the first explicit rational homology classes of Out(F_n) that are neither constant nor Morita classes, advancing understanding of its algebraic structure.

Findings

Computed H_*(Out(F_7);Q) explicitly

Identified new rational homology classes

Extended knowledge of Out(F_n) homology structure

Abstract

We compute the homology groups $H_*(\operatorname{Out}(F_7);\mathbb Q)$ of the outer automorphism group of the free group of rank $7$. We produce in this manner the first rational homology classes of $\operatorname{Out}(F_n)$ that are neither constant ($*=0$) nor Morita classes ($*=2n-4$).