Hyperbolic Dehn Surgery is a procedure for producing closed hyperbolic 3-manifolds from hyperbolic knot complements, by ‘filling in the cusp’ with a solid torus. This procedure produces infinitely many examples of closed hyperbolic manifolds, as Thurston (its discoverer) proved that all but finitely many ways of performing the gluing result in a manifold which admits a hyperbolic structure.
This talk provides a graduate-student-friendly introduction to this area of mathematics, leading up to the statement (but not proof) of Thurston’s theorem, and placing it in the wider context of geometric topology and geometric group theory.
I’ve given a talk on this general theme twice to a graduate student audience, in the following places:
- UC Davis Graduate Student Colloquium
- Arizona State University, Geometric Group Theory Course
Here are the slides from the most recent version of this talk!