GTiNY2013 Video Series 6/20: Jessica Purcell (2nd day, 3rd Talk on Tuesday 8/13 )

Title: Cusp volumes of alternating knots

2nd day, 3rd Talk on Tuesday 8/13
Speaker: Jessica Purcell (Brigham Young University)
Coauthors: Marc Lackenby

We show that the cusp volume of a hyperbolic alternating knot can be bounded above and below in terms of the twist number of an alternating diagram of the knot. This answers in the affirmative a question asked by Thistlethwaite over a decade ago on the cusp geometry of these knots. In addition to giving diagrammatical estimates on cusp volume, this also leads to geometric estimates on lengths of slopes, in terms of a diagram of the knot. All these estimates are explicit. This is joint work with Marc Lackenby.