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Does annular Khovanov homology detect knots which induce the tight contact structure on S^3?
Geometry/Topology| Speaker: | Ian Banfield, Boston College |
| Location: | 2112 MSB |
| Start time: | Mon, May 15 2017, 1:10PM |
A beautiful result by Hedden building on work of Rudolph states that the fibered links inducing the tight contact structure on \(S^3\) are exactly the fibered strongly quasipositive braid closures. The knot Floer complex detects membership in the class of fibered strongly quasipositive braid closures, and one can ask the question if this is also the case for Khovanov-theoretic invariants.
I will state a conjecture involving the annular refinement of Khovanov homology and outline a strategy towards a proof, using a new characterization of a class of fibered strongly quasipositive braids closures in braid-theoretic terms and the \(\mathfrak{sl_2}\) structure on sutured Khovanov homology. This is work in progress and I will explain partial results, including the positive braid and 3-braid cases.