Quasi-morphisms on cotangent bundles and symplectic homogenization
Symplectic Geometry
2011-10-25 v2 Dynamical Systems
Abstract
For a class of closed manifolds N, we construct a family of functions on the Hamiltonian group G of the cotangent bundle T*N. These restrict to homogeneous quasi-morphisms on the subgroup generated by Hamiltonians with support in a given cotangent ball bundle. The family is parametrized by the first real cohomology of N, and in the case N=T^n, it coincides with Viterbo's symplectic homogenization operator. These functions have applications to the algebraic and geometric structure of G and its subgroups, to symplectic rigidity, and to Aubry-Mather and weak KAM theory.
Keywords
Cite
@article{arxiv.1104.4928,
title = {Quasi-morphisms on cotangent bundles and symplectic homogenization},
author = {Alexandra Monzner and Nicolas Vichery and Frol Zapolsky},
journal= {arXiv preprint arXiv:1104.4928},
year = {2011}
}
Comments
The paper has been withdrawn because the class of admissible manifolds cannot be currently shown to be nonempty