• Corpus ID: 244715001

# The surface category and tropical curves

@inproceedings{Steinebrunner2021TheSC,
title={The surface category and tropical curves},
author={Jan Steinebrunner},
year={2021}
}
We compute the classifying space of the surface category $\mathrm{Cob}_2$ whose objects are closed $1$-manifolds and whose morphisms are diffeomorphism classes of surface bordisms, and show that it is rationally equivalent to a circle. It is hence much smaller than the classifying space of the topologically enriched surface category $\mathcal{C}_2$ studied by Galatius-Madsen-Tillmann-Weiss. However, we also show that for the wide subcategory \$\mathrm{Cob}_2^{\chi\le0} \subset \mathrm{Cob}_2…