Miriam Kuzbary, Rice University
A New Concordance Group of Links
3:30 pm, Tuesday, September 26, TUC 352
The knot concordance group has been the subject of much study since its introduction by Ralph Fox and John Milnor in 1966. One might hope to generalize the notion of a concordance group to links; however, the immediate generalization to the set of links up to concordance does not form a group since connected sum of links is not well-defined. In 1988, Jean Yves Le Dimet defined the string link concordance group, where a link is based by a disk and represented by embedded arcs in D^2 × I. In 2012, Andrew Donald and Brendan Owens defined groups of links up to a notion of concordance based on Euler characteristic. However, both cases expand the set of links modulo concordance to larger sets and each link has many representatives in these larger groups. In this talk, I will present joint work with Matthew Hedden where we define a link concordance group based on the the “knotification” construction of Peter Ozsváth and Zoltán Szabó, giving a definition of a link concordance group where each link has a unique group representative. I will also present new invariants for studying this group which use group theory and Heegaard-Floer homology.