Fragmented Hofer's geometry on Hameomorphism groups and its application

2016/12/04 by Kawasaki, Morimichi
#FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1612.01107

Abstract

Stefan Muller posed the problem "Do Hofer's metrics on the group of Hamiltonian diffeomorphism and the one of Hamiltonian homeomorphisms (Hameomorphisms) correspond?". Let (M,ω) be a compact exact symplectic manifold. We prove that the group of Hamiltonian homeomorphisms is not a simple group if the positive answer of Muller's question holds . To prove this results, we introduce fragmented Hofer's norms on a normal subgroup of the group of Hamiltonian homeomorphisms.

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