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 language | English |
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Pages (from-to) | 205-249 |
Number of pages | 45 |
Journal | Journal of Modern Dynamics |
Volume | 6 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2012 |
Externally published | Yes |
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Applied Mathematics