# The knot complement problem for nullhomotopic knots

## Location

383-N

Tuesday, May 10, 2022 4:00 PM

Aliakbar Daemi (Washington University in St. Louis)

In their celebrated work, Gordon and Luecke proved that knots in the three-dimensional sphere are determined by their complements. Subsequently, Boileau asked whether the same result holds for null-homotopic knots in arbitrary 3-manifolds. In this talk, I will discuss a program to answer this question. In particular, I will explain how one can give an affirmative answer to Boileau's question for knots in some families of 3-manifolds. This is joint work with Tye Lidman.