Geometry & Topology
- Geom. Topol.
- Volume 19, Number 1 (2015), 365-411.
Quasimorphisms on contactomorphism groups and contact rigidity
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.
Geom. Topol., Volume 19, Number 1 (2015), 365-411.
Received: 15 August 2013
Revised: 21 January 2014
Accepted: 30 January 2014
First available in Project Euclid: 16 November 2017
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Borman, Matthew Strom; Zapolsky, Frol. Quasimorphisms on contactomorphism groups and contact rigidity. Geom. Topol. 19 (2015), no. 1, 365--411. doi:10.2140/gt.2015.19.365. https://projecteuclid.org/euclid.gt/1510858683