4:00 pm Thursday, February 17, 2011

Cameron Gordon (UT Austin)

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* ≥ 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.)