Contact Homology, Capacity and Non-Squeezing in R^2n x S^1 via Generating Functions

Abstract

Starting from the work of Bhupal, we extend to the contact case the Viterbo capacity and Traynor's construction of symplectic homology. As an application we get a new proof of the Non-Squeezing Theorem of Eliashberg, Kim and Polterovich.

Revised version, to appear in the Annales de l'Institut Fourier

References in corpus (3)

• Functors and Computations in Floer homology with Applications Part II
• Non-negative Legendrian isotopy in $S{T}^{\ast }M$
• Generating family invariants for Legendrian links of unknots

Cited by in corpus (11)

• Non-squeezing property of contact balls
• On iterated translated points for contactomorphisms of R^{2n+1} and R^{2n} x S^1
• Givental's non-linear Maslov index on lens spaces
• Geometric structures on contactomorphism groups and contact rigidity in jet spaces
• Generating families and constructible sheaves
• A contact camel theorem
• Contact spectral invariants and persistence
• An integer valued bi-invariant metric on the group of contactomorphisms of R^2n x S^1
• Contact Hamiltonian dynamics and perturbed contact instantons with Legendrian boundary condition
• Equivariant Homology of Generating Functions and Orderability of Lens Spaces
• On displaceability of pre-Lagrangian fibers in contact toric manifolds