The S_n-Equivariant Rational Homology of the Tropical Moduli Spaces Δ_2,n

Abstract

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

Keywords:

• Tropical geometry
• tropical moduli of curves
• metric graphs
• S_n-representations
• symmetric Δ-complexes

Acknowledgments

I am grateful to Melody Chan for suggesting this direction of research, answering numerous questions, providing useful feedback on my writing, and encouraging me in times of doubt. I thank Christin Bibby and Nir Gadish for discussions on alternative computational methods. I also thank the anonymous referee(s) for providing useful comments to this article. Lastly, I thank Sarah Griffith for many words of encouragement and mathematical discussions.

Declaration of interest

No potential conflict of interest was reported by the author(s).

Notes

1 https://www.math.brown.edu/∼claudia_yun/