Topology Seminar (Introductory Talk): Topological and Geometric Complexity for Hyperbolic 3-Manifolds

Seminar | March 6 | 2-3 p.m. | 740 Evans Hall

 Diane Hoffoss, University of San Diego

 Department of Mathematics

We will introduce Scharlemann-Thompson handle decompositions of a 3-manifold, and a generalization of this which we call a graph decomposition. Using these, we define topological measures of complexity for the manifold. In the case where the manifold has additional metric structure, we use Morse and Morse-like functions to give geometric definitions of complexity as well. We then show that some of these geometric and topological complexities are linearly related for hyperbolic 3-manifolds.