Quasimorphisms on contactomorphism groups and contact rigidity

Matthew Strom Borman, Frol Zapolsky

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)365-411
Number of pages47
JournalGeometry and Topology
Volume19
Issue number1
DOIs
StatePublished - Feb 27 2015

ASJC Scopus subject areas

  • Geometry and Topology

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