Topology Seminar (Introductory Talk): Thin position and additive invariants of knots

Seminar | April 5 | 2:10-3 p.m. | 736 Evans Hall

 Scott Taylor, Colby College

 Department of Mathematics

Seifert genus and bridge number are classical knot invariants that detect the unknot and are additive under connected sum. Other classical knot invariants such as tunnel number, higher genus bridge number, and Gabai width have more complicated stories. I'll review the definitions of these invariants and their (non-)additivity properties. Additionally, I'll explain Scharlemann-Thompson thin position for 3-manifolds and its connection to Gabai's thin position for knots in the 3-sphere.