Europe/Lisbon
Room P3.10, Mathematics Building — Online

Yonatan Harpaz

Yonatan Harpaz, CNRS at University of Paris 13
The cobordism hypothesis in dimension 1

The cobordism hypothesis is a conjectural characterization of the framed cobordism $(\infty,n)$-category as the free symmetric monoidal $(\infty,n)$-category with duals generated by a single object. After its original formulation by Baez and Dolan in 1995, a strategy for a proof of the conjecture was put forward by Lurie in 2009. Though this strategy is very efficient in reducing the general hypothesis to a relatively concrete statement (Claim 3.4.17 in Lurie's text), a formal proof of this concrete statement has yet to appear in the literature. In addition, this strategy does not cover the 1-dimensional case. In this talk I will describe a way to extend Lurie's strategy to the case of $n = 1$, in which case the analogue of the missing claim can be proved using, among other things, the notion of quasi-unital $\infty$-categories.

Additional file

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Yonatan's slides.

Local participants are invited to join us in room 3.10 (3rd floor, Mathematics Department, Instituto Superior Técnico).