Dehn filling techniques in hyperbolic knot theory
by
Jessica Purcell
Brigham Young University

In these three talks, we explain how Dehn filling techniques can give geometric bounds on hyperbolic knots and links in the 3-sphere.

We start by examining a class of links called "augmented links" which have a very explicit hyperbolic structure, and see that every knot and link complement can be obtained by Dehn filling these links. We will compute hyperbolic structures on these link complements, and give bounds on their volumes and cusp shapes.

Next, we will discuss results bounding change in hyperbolic structure under Dehn filling, including changes in volume. We will apply these results to the augmented links to obtain bounds on volume for many classes of knots and links in the 3--sphere.

Finally, we will examine additional applications of the Dehn filling results, including to classes of "multiply twisted" knots.

Date received: May 28, 2009