Skip to main content

Exotic Mazur manifolds and knot trace invariants

Posted in
Lisa Piccirillo
UC Austin
Mon, 2019-09-16 15:00 - 15:50
MPIM Lecture Hall

From a handlebody-theoretic perspective, the simplest compact, contractible 4-manifolds, other than the 4-ball, are Mazur manifolds. We produce the first pairs of Mazur manifolds that are homeomorphic but not diffeomorphic. Our diffeomorphism obstruction comes from our proof that the knot Floer homology concordance invariant $\nu$ is an invariant of a particular 4-manifold associated to the knot, called the knot trace. As a corollary, we produce integer homology 3-spheres admitting two distinct $S^1\times S^2$ surgeries, resolving a question from Problem 1.16 in Kirby's list. This is joint work with Kyle Hayden and Tom Mark.

© MPI f. Mathematik, Bonn Impressum & Datenschutz
-A A +A