Quasimorphisms on contactomorphism groups and contact rigidity

Matthew Strom Borman, Frol Zapolsky

Research output: Contribution to journalArticlepeer-review


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

Bibliographical note

Publisher Copyright:
© 2015, Mathematical Sciences Publishers. All rights reserved.

ASJC Scopus subject areas

  • Geometry and Topology


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