Topology Seminar: Knots and exotic structures

Seminar | August 26 | 4:10-5 p.m. | 3 Evans Hall

 Selman Akbulut, Michigan State

 Department of Mathematics

Given a knot $K$, let $K^r$ be the 4-manifold obtained by attaching a 2-handle to $B^4$ with framing $r$. I will discuss the status of the following problem (which has many versions): Can you find non-concordant knots $K, L$ so that $K^r$ and $L^r$ are diffeomorphic to each other?, or not diffeomorphic to each other? (i.e. $K^r$ and $L^r$ are exotic copies of each other). I will discuss the 40-year history of this problem, and its relation to corks and Stein structures, including the recent progress by Yasui (relating the difficult case of $r=0$).