Coordinates: JH Michell Theatre in the Richard Berry Building
Speaker: William Jaco (Oklahoma State University)
Title: Constructing annular-efficient triangulations
Abstract: (Joint work with Hyam Rubinstein.)

A triangulation of a compact 3-manifold is annular-efficient if it is 0-efficient and the only normal annuli with essential boundary are thin edge-linking. If a compact 3-manifold has an annular-efficient triangulation, then it is irreducible, boundary-irreducible, and an-annular. Conversely, it is shown that for a compact, irreducible, boundary-irreducible, and an-annular 3-manifold, any triangulation can be modified to an annular-efficient triangulation. It follows that for a manifold satisfying this hypothesis, there are only a finite number of boundary slopes for incompressible and boundary-incompressible surfaces of a bounded Euler characteristic.