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A genus one algebraically slice knot is 1-solvable

Banff International Research Station for Mathematical Innovation and Discovery

Joint with Taylor Martin, Carolyn Otto, and Jung Hwan Park. In the 1990's Cochran Orr and Teichner introduced a filtration of knot concordance indexed by half integers (the solvable filtration.)  Since then this filtration has been a convenient setting for many advances in knot concordance.  There are now many results in the literature demonstrating the difference between the n'th and (n.5)'th terms in this filtration, but none regarding the difference between the (n.5)'th and (n+1)'st.  In this talk we will prove that every genus one (0.5)-solvable knot is 1-solvable.  We will also provide a new sufficient condition for a high genus (0.5)-solvable knot to be 1-solvable and close with some possible candidates for knots which are (0.5)-solvable but not 1-solvable.

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

video/mp4

Author affiliation: University of Wisconsin - Eau Claire

2016-08-26

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58990

Unreviewed

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