Non-degeneracy of Legendrians from bifurcation of contact homology

Abstract: We show that the invariance of Legendrian contact homology can be formulated in terms of a bifurcation analysis whose action properties are continuous with respect to the oscillatory norm of the contact Hamiltonian. (I.e. the barcode varies continuously with respect to the same.) Combined with work of Rosen-Zhang this implies non-degeneracy of the Shelukhin-Chekanov-Hofer metric on the space of Legendrian embeddings. We also explain how convex surface techniques in dimension three can be used to prove a statement related to the converse: a non-Legendrian knot cannot be approximated by the image of a Legendrian knot under a sequence of C0-converging contactomorphisms. This is joint work with M. Sullivan.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

Series comments: On the week of the seminar, an announcement with the Zoom link is mailed to the seminar mailing list. To receive these e-mails, please sign up by writing to Lev Buhovsky (http://www.math.tau.ac.il/~levbuh/).