Fragmented Hofer's geometry on Hameomorphism groups and its application

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.

The present paper is withdrawn because the main result follow by a straightforward argument

References in corpus (3)

• On the uniqueness of generating Hamiltonian for continuous limits of Hamiltonians flows
• Locality of continuous Hamiltonian flows and Lagrangian intersections with the conormal of open subsets
• Fragmented Hofer's geometry