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Mon, 08 Jun 2026
15:30
L5

Dehn Surgery and Algorithms

Misha Schmalian
((Mathematical Institute University of Oxford))
Abstract

Dehn Surgery is an operation on 3-manifolds that is ubiquitous in the field of low-dimensional topology. Concretely, given a link L in a 3-manifold N, Dehn surgery produces many new 3-manifolds. A classical result of Lickorish-Wallace states that from one fixed 3-manifold N one can obtain all other 3-manifolds by Dehn surgery using some link in N. However it remains unclear, in general, which manifolds can be obtained by Dehn surgery using a fixed manifold N and a fixed link L. I will discuss how one can algorithmically decide this question and then discuss applications of this algorithm.