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.
|Number of pages||47|
|Journal||Geometry and Topology|
|State||Published - 27 Feb 2015|
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© 2015, Mathematical Sciences Publishers. All rights reserved.
ASJC Scopus subject areas
- Geometry and Topology