Quasi-morphisms on cotangent bundles and symplectic homogenization

2011/04/26 by Alexandra Monzner, Monzner, Alexandra, Nicolas Vichery +3 · 1 citation
Mathematics · #37J50 #53D40 #70H20 #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1104.4928

openalex publication_date 2011/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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=Tⁿ, 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.

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