Partial quasimorphisms and quasistates on cotangent bundles, and symplectic homogenization

Alexandra Monzner, Nicolas Vichery, Frol Zapolsky

Research output: Contribution to journalArticlepeer-review

Abstract

For a closed connected manifold N, we construct a family of functions on the Hamiltonian group G of the cotangent bundle T * N, and a family of functions on the space of smooth functions with compact support on T * N. These satisfy properties analogous to those of partial quasimorphisms and quasistates of Entov and Polterovich. The families are parametrized by the first real cohomology of N. In the case N=T n the family of functions on G coincides with Viterbo's symplectic homogenization operator. These functions have applications to the algebraic and geometric structure of G, to Aubry-Mather theory, to restrictions on Poisson brackets, and to symplectic rigidity.

Original languageEnglish
Pages (from-to)205-249
Number of pages45
JournalJournal of Modern Dynamics
Volume6
Issue number2
DOIs
StatePublished - Apr 2012
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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