Contact non-squeezing via selective symplectic homology

Abstract: In this talk, I will introduce a new version of symplectic homology, called "selective symplectic homology", that is associated to a Liouville domain and an open subset of its boundary. The selective symplectic homology is obtained as the direct limit of Floer homology groups for Hamiltonians whose slopes tend to infinity on the open subset but remain close to 0 and positive on the rest of the boundary.

I will show how selective symplectic homology can be used to prove contact non-squeezing phenomena. One such phenomenon concerns homotopy spheres that can be filled by a Weinstein domain with infinite dimensional symplectic homology: there exists a (smoothly) embedded closed ball in such a sphere that cannot be contactly squeezed into every non-empty open subset. As a consequence, there exists a contact structure on the standard smooth sphere (in certain dimensions) that is homotopic to the standard contact structure but which exhibits non-trivial contact non-squeezing.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

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