• Corpus ID: 244715001

The surface category and tropical curves

  title={The surface category and tropical curves},
  author={Jan Steinebrunner},
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… 
1 Citations

Labelled cospan categories and properads

We prove Steinebrunner’s conjecture on the biequivalence between (colored) properads and labelled cospan categories. The main part of the work is to establish a 1-categorical, strict version of the