On the autonomous metric on groups of Hamiltonian diffeomorphisms of closed hyperbolic surfaces

2013/05/13 by Michael Brandenbursky, Brandenbursky, Michael · 2 citations
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG) #math.GT #math.SG

paper · pdf · doi:10.48550/arxiv.1305.2757

Now it is a part of arXiv:1405.7931

arxiv created 2014/05/30 · arxiv updated 2014/06/03

Abstract

Let Σ_g be a closed hyperbolic surface of genus g and let Ham(Σ_g) be the group of Hamiltonian diffeomorphisms of Σ_g. The most natural word metric on this group is the autonomous metric. It has many interesting properties, most important of which is the bi-invariance of this metric. In this work we show that Ham(Σ_g) is unbounded with respect to this metric.

Citations

• On the L^p-geometry of autonomous Hamiltonian diffeomorphisms of surfaces

Cited by

• Random Hamiltonians I: Probability measures and random walks on the Hamiltonian diffeomorphism group
• On the L^p-geometry of autonomous Hamiltonian diffeomorphisms of surfaces

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