Special Surfaces in Knot Complements

William Marsh Rice University, Houston TX

Investigators

Abstract

Tomova's research centers on Heegaard splittings of 3-dimensional manifolds and bridge surfaces for knots in manifolds. Given a knot in a closed 3-manifold, a bridge surface is a surface that decomposes the manifold into handlebodies and also cuts the knot into simple arcs. In the last year and a half Tomova has proven several important results about the behavior of bridge surfaces. She intends to extend and generalize her results and apply her work to several open problems in the area. With the discovery of the DNS molecule and the recent advent of string theory, the study of knots has come to the forefront of modern science. Knot Theory is a subarea of Topology which studies the properties of knotted strings and is the main area of interest of Maggy Tomova. Her study of knots also requires an understanding of 3-manifolds, objects that locally look like 3-dimensional space.