On continuity of quasimorphisms for symplectic maps

Michael Entov*, Leonid Polterovich, Pierre Py, Michael Khanevsky

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

We discuss C0-continuous homogeneous quasimorphisms on the identity component of the group of compactly supported symplectomorphisms of a symplectic manifold. Such quasimorphisms extend to the C0-closure of this group inside the homeomorphism group. We show that for standard symplectic balls of any dimension, as well as for compact oriented surfaces other than the sphere, the space of such quasimorphisms is infinite-dimensional. In the case of surfaces, we give a user-friendly topological characterization of such quasimorphisms. We also present an application to Hofer’s geometry on the group of Hamiltonian diffeomorphisms of the ball.

Original languageEnglish
Title of host publicationProgress in Mathematics
PublisherSpringer Basel
Pages169-197
Number of pages29
DOIs
StatePublished - 2012

Publication series

NameProgress in Mathematics
Volume296
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X

Funding

FundersFunder number
National Science FoundationDMS-0905911
Israel Science Foundation509/07, 881/06

    Keywords

    • Calabi homomorphism
    • Hofer metric
    • Quasimorphism
    • Symplectomorphism

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