Geometry and Topology Seminar: "Braids, foliations, and exotically knotted surfaces"

Abstract: Four-manifold topology is famous for "exotic" phenomena, like non-standard smooth structures on Euclidean 4-space. However, this wild flexibility often evaporates in the presence of geometry, such as complex or symplectic structures. In this talk, we'll explore this phase transition using braids and singular foliations on surfaces in 4-manifolds. As an application, I will describe smoothly (indeed, holomorphically) embedded surfaces in the 4-ball that are "exotically knotted", i.e., isotopic through ambient homeomorphisms but not diffeomorphisms.

Host: Aliakbar Daemi