Andrew Brasile : Boundary Slopes of Knot Complements

Posted by Paul Reschke , part of the Graduate Student Colloquium.

At

April 9, 2012, 4:15 p.m.

In

SEO 636

Abstract

The set of boundary slopes of essential surfaces of a knot complement has been the object of study for several decades. It is an important invariant of the knot and has applications to Dehn fillings and the Neuwirth Conjecture. Studying this set makes use of theory from a surprising variety of fields including complex analysis, tropical geometry, linear algebra and group theory. We will establish these applications and connections to other fields and finally discuss an approach for finding the set of boundary slopes of essential surfaces of knot complements. This talk is intended to be accessible for graduate students of all levels; no technical knowledge of knot theory is expected.