The $S_n$-equivariant rational homology of the tropical moduli spaces $\Delta_{2,n}$

TL;DR

This paper calculates the symmetric group-equivariant rational homology of tropical moduli spaces _{2,n} for small n, providing explicit computational results using Sage software.

Contribution

It introduces a method to compute the equivariant rational homology of tropical moduli spaces _{2,n} for n \u2264 8, combining combinatorial and computational techniques.

Findings

Explicit homology computations for _{2,n} with n  8

Development of a cellular chain complex approach for symmetric -complexes

Implementation of calculations in Sage software

Abstract

We compute the $S_n$-equivariant rational homology of the tropical moduli spaces $\Delta_{2,n}$ for $n\leq 8$ using a cellular chain complex for symmetric $\Delta$-complexes in Sage.