Quasi-morphisms on contactomorphism groups and contact rigidity
arXiv:1308.3224 · doi:10.2140/gt.2015.19.365
Abstract
We build homogeneous quasi-morphisms on the universal cover of the contactomorphism group for certain prequantizations of monotone symplectic toric manifolds. This is done using Givental's nonlinear Maslov index and a contact reduction technique for quasi-morphisms. We show how these quasi-morphisms lead to a hierarchy of rigid subsets of contact manifolds. We also show that the nonlinear Maslov index has a vanishing property, which plays a key role in our proofs. Finally we present applications to orderability of contact manifolds and Sandon-type metrics on contactomorphism groups.
40 pages, 1 figure; v3: added proof of C^0 continuity, minor corrections. To appear in Geometry & Topology
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Cited by in corpus (9)
- Contact Hamiltonian Systems
- Universal orderability of Legendrian isotopy classes
- Quasi-morphisms and quasi-states in symplectic topology
- Vanishing of Rabinowitz Floer homology on negative line bundles
- Givental's non-linear Maslov index on lens spaces
- Contactomorphism groups and Legendrian flexibility
- Bi-invariant metrics on contactomorphism groups
- Rabinowitz Floer homology of negative line bundles and Floer Gysin sequence
- Translated points for contactomorphisms of prequantization spaces over monotone symplectic toric manifolds