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Universität Augsburg
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Universität Augsburg
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Dr. Jan Steinebrunner
University of Oxford
spricht am
Montag, 5. Juli 2021
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16 Uhr s.t.
im
Zoom (hybride Veranstaltung)
über das Thema:
| Abstract: |
| The surface cobordism category $\mathrm{Cob}_2$ has as objects disjoint unions of circles and as morphisms diffeomorphism classes of surface bordisms. Such cobordism categories were popularised in the 80s through Atiyah and Segal's work on topological and conformal field theories, and have since appeared in various forms throughout mathematical physics and algebraic topology. While cobordisms in dimension 2 are in principle easy to understand (by the classification of surfaces) I will argue that the algebraic structure of how they are glued nevertheless leads to interesting moduli spaces. I will recall the notion of a classifying space of a category and show that $B(\mathrm{Cob}_2)$ contains copies of the moduli spaces of tropical curves. Concretely, I will introduce a certain subcategory $\mathrm{Cob}_2^{\chi\le0} \subset \mathrm{Cob}_2$ and construct explicit splitting maps from $B(\mathrm{Cob}_2^{\chi\le0})$ to a free infinite loop space on tropical moduli space $\Delta_g$ for all $g \ge 2$. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Wolfgang Steimle |