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C0–Symplectic Geometry Under Displacements
*Stéphane TchuiagaCorresponding authortchuiagas@gmail.comDepartment of MathematicsUniversity of BueaSouth West Region, CameroonView full profile →
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- Received:
- 26 Jun 2018
- Accepted:
- 08 Sep 2018
- Published Online:
- 16 May 2019
- Article type:
- Article
- Language:
- EN
- Article no.:
- 1726037X.2018.1551717
- Pages:
- 109–129
Abstract
This paper continues the study of the group Hameo(M, ω), of all Hamiltonian homeomorphisms of a closed symplectic manifold (M, ω). After given a direct proof of the positivity result of the symplectic displacement energy, we show that the uniqueness theorem of generators of strong symplectic isotopies extends to any closed symplectic manifold: An explicit formula for the mass flow of any strong symplectic isotopy with respect to its generator is given. We show that Hameo(M, ω) inherits under the C0 -Hamiltonian topology, the fragmentation property, the algebraic perfectness, and coincides with the commutator sub-group of the group of all strong symplectic homeomorphisms. This solves a Banyaga's conjecture, and some other conjectures are also formulated.
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