Fragmented Hofer's geometry on Hameomorphism groups and its application

Morimichi Kawasaki

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arXiv · 1612.01107

Fragmented Hofer's geometry on Hameomorphism groups and its application

Morimichi Kawasaki

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Abstract

Stefan M$\ddot{\mathrm{u}}$ller posed the problem "Do Hofer's metrics on the group of Hamiltonian diffeomorphism and the one of Hamiltonian homeomorphisms (Hameomorphisms) correspond?". Let $(M,\omega)$ be a compact exact symplectic manifold. We prove that the group of Hamiltonian homeomorphisms is not a simple group if the positive answer of M$\ddot{\mathrm{u}}$ller'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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Morimichi Kawasaki. 2016-12-04. Fragmented Hofer's geometry on Hameomorphism groups and its application. https://arxiv.org/abs/1612.01107

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