Stabilization distance bounds from link Floer homology

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• Andras Juhasz, Oxford
• Wednesday 28 November 2018, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

We consider the set of connected surfaces in the 4-ball that bound a fixed knot in the 3-sphere. We define the stabilization distance between two surfaces as the minimal g such that we can get from one to the other using stabilizations and destabilizations through surfaces of genus at most g. Similarly, we obtain the double point distance between two surfaces of the same genus by minimizing the maximal number of double points appearing in a regular homotopy connecting them.

To many of the concordance invariants defined using Heegaard Floer homology, we construct an analogous invariant for a pair of surfaces. We show that these give lower bounds on the stabilization distance and the double point distance. We compute our invariants for some pairs of deform-spun slice disks by proving a trace formula on the full infinity knot Floer complex, and by determining the action on knot Floer homology of an automorphism of the connected sum of a knot with itself that swaps the two summands. This is joint work with Ian Zemke.

This talk is part of the Differential Geometry and Topology Seminar series.

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