## 3-Manifold Seminar: The Gordon-Luecke Theorem

Seminar | October 24 | 11:10 a.m.-12:30 p.m. | 939 Evans Hall

Alois Cerbu, UC Berkeley

Department of Mathematics

Cameron Gordon and John Luecke proved that knots are determined by their complements, in the following sense: for smooth knots $K$ and $K' \subset S^3$ whose complements are homeomorphic, there exists a self-homeomorphism of $S^3$ taking $K$ to $K'$. In fact, if this homeomorphism is orientation-preserving, then $K$ and $K'$ will be isotopic. We will examine the proof from their 1989 paper.

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