## Geometry & Topology

### Quasimorphisms on contactomorphism groups and contact rigidity

#### 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.

#### Article information

Source
Geom. Topol., Volume 19, Number 1 (2015), 365-411.

Dates
Revised: 21 January 2014
Accepted: 30 January 2014
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.gt/1510858683

Digital Object Identifier
doi:10.2140/gt.2015.19.365

Mathematical Reviews number (MathSciNet)
MR3318754

Zentralblatt MATH identifier
1312.53109

#### Citation

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

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