Systems of Whitney disks and diffeomorphisms of $S^4$ (David Gay)

PATCH Seminar (join with Bryn Mawr, Haverford, Penn, and Swarthmore)

Abstract: This is a report on work in progress with David Gabai and Daniel Hartman. Our goal is to show that there exists an orientation preserving diffeomorphism of $S^4$ that is not isotopic to the identity. I will outline the proposed proof and then focus on the key underlying combinatorial data used to construct an invariant: systems of Whitney disks for intersecting spheres in connected sums of $S^2 \times S^2$'s. I will explain what these are, how they relate to diffeomorphisms of $S^4$, and what the moves are that relate systems of disks describing isotopic diffeomorphisms, which are the moves that any invariant constructed this way need to be invariant under.

In the morning background talk (11am, in DRL A6), I will give an introduction to pseudoisotopies and parameterized Morse theory (a.k.a. Cerf theory).