Exotic spheres in four manifolds
Speaker:
Hannah Schwartz, Bryn Mawr College
Date and Time:
Tuesday, July 9, 2019 - 11:00am to 12:00pm
Location:
Fields Institute, Room 230
Abstract:
Throughout the talk, we will compare the notions of topological isotopy, smooth isotopy, and smooth equivalence (via an ambient diffeomorphism preserving homology) between homotopic 2-spheres smoothly embedded in a 4-manifold. In particular, we will discuss pairs of spheres that are 1) both topologically isotopic and smoothly equivalent, but not smoothly isotopic, and 2) smoothly equivalent but not topologically isotopic. Indeed, the examples satisfying condition 2) show that Gabai's recent "4D Lightbulb Theorem" does not hold without the 2-torsion hypothesis.