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A. Daemi 10-3-2022

Title: The knot complement problem for nullhomotopic knots.
Abstract: 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 arbitrary knots in some families
of 3-manifolds including any connected sum of Brieskorn homology spheres.
This is joint work with Tye Lidman.

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