Tropicalizing the moduli space of spin curves

We study the tropicalization of the moduli space of algebraic spin curves, S ¯ g , n . We exhibit its combinatorial stratification and prove that the strata are irreducible. We construct the moduli space of tropical spin curves S ¯ g , n trop , prove that is naturally isomorphic to the skeleton of the analytification, S ¯ g , n an , of S ¯ g , n , and give a geometric interpretation of the retraction of S ¯ g , n an onto its skeleton in terms of a tropicalization map S ¯ g , n an → S ¯ g , n trop .