Abstract
We build homogeneous quasimorphisms 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 quasimorphisms. We show how these quasimorphisms 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.
Citation
Matthew Strom Borman. Frol Zapolsky. "Quasimorphisms on contactomorphism groups and contact rigidity." Geom. Topol. 19 (1) 365 - 411, 2015. https://doi.org/10.2140/gt.2015.19.365
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