Title: Knots, surfaces and 3-manifolds
Abstract: The study of 1- and 2-manifolds, and related objects, plays an important role within 3-manifold topology, both as tools and as objects of interest in their own right. Central to this is knot theory, which focuses on 1-manifolds within the 3-sphere. In this talk we will discuss some results in these familiar dimensions, including a relationship between the Alexander polynomial of a homogeneous link and its Seifert surfaces, and the Birman exact sequence for the mapping class group of a 3-manifold.