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A new concordance group of links

Banff International Research Station for Mathematical Innovation and Discovery

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 Ozsv´ath and Zoltan Szab´o, giving a definition of a link concordance group where each link has a unique group representative. I will also present invariants for studying this group using both group theory and Heegaard-Floer Homology.

Mathematics; Manifolds and cell complexes; Differential geometry; Low dimensional topology

video/mp4

Author affiliation: Rice University

2018-02-01

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64516

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/