# An obstruction to concordance to boundary links

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Chris Davis, University of Wisconsin-Eau Claire
Fine Hall 314

In-Person and Online Talk

In a pair of celebrated papers from 1990's Cochran-Orr and Livingston produced links with vanishing Milnor invariants which are not concordant to boundary links.  The examples they produce sit in a larger family called homology boundary links.  It is still unknown if every link with vanishing Milnor invariants is concordant to a homology boundary link.  During this talk I will produce an invariant which might be able to detect such a difference.  Along the way we will study the interaction of boundary links, homology boundary links, and Milnor's invariants with the solvable filtration of knot concordance introduced by Cochran-Orr-Teichner in 2003, and prove that any homology boundary link is related by concordance and a strong notion of S-equivalence.

This work is joint with Shelly Harvey and JungHwan Park.