Title: On rationally slice knots Abstract: A knot in the three-sphere is called slice if it bounds a smooth disk in the four-ball. If one only requires the disk to be in a rational homology four-ball, then we say that the knot is rationally slice. We present a rationally slice knot which is not slice even

Title: Abstract Infinite Group Theory in Linear Groups. Abstract: It is a classical result that the commutator subgroup of a group $G$ is finite whenever such is the factor group $G/Z(G)$. In general, this result cannot be reverted: there are (soluble) groups with a finite commutator subgroup but an infinite factor over the centre. However,

Title: A contact invariant from bordered Heegaard Floer homology Abstract: Given a contact structure on a bordered 3-manifold, we describe an invariant which takes values in the bordered sutured Floer homology of the manifold. This invariant satisfies a nice gluing formula, and recovers the Oszvath-Szabo contact class in Heegaard Floer homology. This is joint work

Title: A combinatorial description of the knot concordance invariant epsilon Abstract: Sitting at the intersection of 4-dimensional topology and knot theory, the knot concordance group is an important object in low-dimensional topology whose structure is not yet fully explored and understood. One approach to study knot concordance is to use knot Floer homology, introduced by

Title: The co-rank of three-dimensional homology handlebody groups Abstract: A group G is called very large if G has a non-abelian free quotient.  We examine the question of which three-manifolds have very large fundamental group.  This question is especially subtle for a three-dimensional homology handlebody of genus g, since the fundamental group of such a