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arXiv · 1111.0287

Partial quasi-morphisms and quasi-states on cotangent bundles, and symplectic homogenization

Alexandra Monzner·Nicolas Vichery·Frol Zapolsky
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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 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.

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Alexandra Monzner, Nicolas Vichery, Frol Zapolsky. 2011-11-01. Partial quasi-morphisms and quasi-states on cotangent bundles, and symplectic homogenization. https://arxiv.org/abs/1111.0287

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