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BIRS Workshop Lecture Videos

Knot filtration on ECH Hutchings, Michael


Given a transverse knot in \(S^3\), together with an irrational number, one can define a filtration on the embedded contact homology of \(S^3\). This filtration is functorial with respect to symplectic cobordisms between transverse knots. Not much is known about this filtration in general (although it might be interesting to try to relate it to filtrations coming from Heegaard Floer theory). However the computation of this filtration for the unknot has significant implications for two-dimensional dynamics. Namely, for an area-preserving map of the disk, the filtration allows us to relate the mean action of periodic orbits to the Calabi invariant.

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