Groups around 3-manifolds minicourse

Lectures by Nathan Dunfield at the Groups around 3-manifolds workshop at CRM during June 5-9, 2023.

Lecture 1

General background about the the topology and geometry of 3-manifolds, including the statement of the Geometrization Theorem. This lecture is intended to provide a common base of knowledge for all the mini-courses, not just this one.

Lecture 2

Solvability of the homeomorphism problem for 3-manifolds. Practical demonstration.

Lecture 3

Finding hyperbolic structures by solving Thurston's gluing equations.

Lecture 4

Fun with finite-covers of 3-manifolds: A story of topology, geometry, and arithmetic. Basically, torsion growth in towers of finite covers a la Bergeron-Venkatesh, Lê, and Lück.