U. Haifa Topology & Geometry seminar: Wednesday, December 24, 2025, 12:00. Speaker: Leor Neuhauser (Hebrew University). Title: “The multiplicaticative structure of higher cobordism categories”.
Cobordisms, a fundamental concept of differential topology, play a deep role in both homotopy theory and higher category theory. In homotopy theory, (framed) n-manifolds up to cobordism are isomorphic to the n-th stable homotopy group of spheres. This isomorphism preserves the graded ring structure, with addition corresponding to disjoint union of manifolds and multiplication corresponding to products of manifolds. In the context of higher categories, there is an (∞, n)-category Bordn of (framed) 0-manifolds, with 1-bordisms between them, 2-bordism between bordisms, and so on up to dimension n. The cobordism hypothesis posits that Bordn is the free fully-dualizable (∞, n)-category on a single generator. While the additive structure of disjoint union naturally lifts to a symmetric monoidal structure on Bordn, lifting the multiplicative structure is more subtle. In this talk, I will describe how we construct this multiplicative structure, and how it relates to the cobordism hypothesis.
Recording:
