%0 Journal Article
%T Partial quasi-morphisms and quasi-states on cotangent bundles, and symplectic homogenization
%A Alexandra Monzner
%A Nicolas Vichery
%A Frol Zapolsky
%J Mathematics
%D 2011
%I arXiv
%X 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 quasi-morphisms and quasi-states 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.
%U http://arxiv.org/abs/1111.0287v1