Elisanda Grigsby
Columbia University
Abstract: Let $K \subset (S^3=\partial B^4)$ be a classical knot. The smooth concordance order of $K$ is defined as the smallest $n \in \mathbb{Z}_+$ for which the connected sum of $n$ copies of $K$ bounds a smoothly-imbedded disk in $B^4$.
I will describe two new invariants which yield an obstruction to a knot having finite smooth concordance order. These invariants are defined by examining analogues of "classical'' Heegaard Floer homology invariants in the double-branched cover of $K$. Using a simple combinatorial description of these invariants in the case where $K$ is a two-bridge knot, we are able to conclude that all two-bridge knots of 12 or fewer crossings for which the concordance order was previously unknown have infinite concordance order.
This is joint work with Daniel Ruberman and Sa\v{s}o Strle.