11/13/2003
Genevieve Walsh
University of Texas at Austin
Some examples of virtually Haken and virtually fibered three-manifolds
Abstract
We show that all two-bridge knot complements and many Montesinos knot complements are virtually fibered. We also prove some results about the existence of virtually Haken Dehn fillings on two-bridge knot complements. Specifically, if a two-bridge knot can be written as a rational knot K_{p/q} with p/q < 1/4, then infinitely many fillings of the knot complement S^3 - K_{p/q} are virtually Haken. The main tool in this work is analyzing covers of the knot complements by geodesic link complements.