The cobordism hypothesis in dimension 1

Abstract: The cobordism hypothesis is a conjectural characterization of the framed cobordism (∞,n)-category as the free symmetric monoidal (∞,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 ∞-categories.

mathematical physicsalgebraic topologycategory theoryquantum algebra

Audience: researchers in the topic

Topological Quantum Field Theory Club (IST, Lisbon)

Series comments: To receive the series announcements, which include the Zoom access password*, please register in
math.tecnico.ulisboa.pt/seminars/tqft/index.php?action=subscribe#subscribe
*the last announcement for a seminar is sent 2 hours before the seminar.
TQFT Club video channel: educast.fccn.pt/vod/channels/k0rk5qewc?locale=en