## Geometry & Topology Seminar - Will Rushworth - Ascent concordance

### Description

HH 312

Speaker: Will Rushworth (McMaster University)

Title: Ascent concordance

Abstract: Let L and L' be links in thickened (closed orientable) surfaces. A concordance between L and L' is a pair (S,M), consisting of a compact orientable 3-manifold M (with appropriate boundary), and S a disjoint union of annuli properly embedded in M x I, cobounding L and L'.

Given such a concordance, how complex need the 3-manifold M be? We shall show that there exist representatives of the same concordance class that are not concordant if one restricts to 3-manifolds that are Morse-theoretically simple.

We shall exhibit an infinite family of such links that are detected by an elementary method, and another such family that cannot be detected in this way. We shall show that an augmented version of Khovanov homology can detect this second family. These links provide counter examples to an analogue of the Slice-Ribbon Conjecture.

Speaker: Will Rushworth (McMaster University)

Title: Ascent concordance

Abstract: Let L and L' be links in thickened (closed orientable) surfaces. A concordance between L and L' is a pair (S,M), consisting of a compact orientable 3-manifold M (with appropriate boundary), and S a disjoint union of annuli properly embedded in M x I, cobounding L and L'.

Given such a concordance, how complex need the 3-manifold M be? We shall show that there exist representatives of the same concordance class that are not concordant if one restricts to 3-manifolds that are Morse-theoretically simple.

We shall exhibit an infinite family of such links that are detected by an elementary method, and another such family that cannot be detected in this way. We shall show that an augmented version of Khovanov homology can detect this second family. These links provide counter examples to an analogue of the Slice-Ribbon Conjecture.

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