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

Abstract: The tropical moduli space \Delta_{g,n} is a topological space that parametrizes isomorphism classes of n-marked stable tropical curves of genus g with total volume 1. Its reduced rational homology has a natural structure of S_n-representations induced by permuting markings. In this talk, we focus on \Delta_{2,n} and compute the characters of these S_n-representations for n up to 8. We use the fact that \Delta_{2,n} is a symmetric \Delta-complex, a concept introduced by Chan, Glatius, and Payne. The computation is done in SageMath.

algebraic geometrycombinatorics

Audience: researchers in the topic

(LAGARTOS) Latin American Real and Tropical Geometry Seminar

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