Cameron Gordon

Department of Mathematics,
University of Texas at Austin,
Austin TX 78712, USA.

Title: L-spaces and left-orderability

Abstract: An important class of 3-manifolds that arise in Heegaard Floer homology theory are the L-spaces, and Ozsváth and Szabó have raised the question of whether these manifolds have a purely topological characterization. We will discuss evidence for the conjecture that a rational homology 3-sphere is an L-space if and only if its fundamental group is not left-orderable.

This is joint work with Steve Boyer and Liam Watson.

Title: Decision problems about higher-dimensional knot groups

Abstract: An $n$-knot is an embedding of the $n$-sphere in the $(n+2)$-sphere, and the corresponding $n$-knot group is the fundamental group of its complement. In contrast to the classical case $n = 1$, we show that many decision problems about the class of $n$-knot groups, $n \geq 3$, (as well as certain classes of groups of other kinds of codimension 2 embeddings) are unsolvable. We also pose some open questions about the class of 2-knot groups, which is still not well understood.

This is joint work with F. González-Acuña and J. Simon.