Published on *Max Planck Institute for Mathematics* (https://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Lisa Piccirillo
Affiliation:

UC Austin
Date:

Mon, 2019-09-16 15:00 - 15:50 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.

**Links:**

[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] https://www.mpim-bonn.mpg.de/node/3444

[3] https://www.mpim-bonn.mpg.de/node/9096