On the group of strong symplectic homeomorphisms

Downloads

DOI:

https://doi.org/10.4067/S0719-06462010000300004

Abstract

We generalize the “hamiltonian topology” on hamiltonian isotopies to an intrinsic “symplectic topology” on the space of symplectic isotopies. We use it to define the group SSympeo (M,ω) of strong symplectic homeomorphisms, which generalizes the group Hameo (M,ω) of hamiltonian homeomorphisms introduced by Oh and Müller. The group SSympeo(M,ω) is arcwise connected, is contained in the identity component of Sympeo(M,ω); it contains Hameo(M,ω) as a normal subgroup and coincides with it when M is simply connected. Finally its commutator subgroup [SSympeo(M,ω), SSympeo(M,ω)] is contained in Hameo(M,ω).

Keywords

Hamiltonian homeomorphisms , hamiltonian topology , symplectic topology , stromg symplectic homeomorphisms , C⁰ symplectic topology
  • Augustin Banyaga Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA.
  • Pages: 49–69
  • Date Published: 2010-10-01
  • Vol. 12 No. 3 (2010): CUBO, A Mathematical Journal

Downloads

Download data is not yet available.

Published

2010-10-01

How to Cite

[1]
A. Banyaga, “On the group of strong symplectic homeomorphisms”, CUBO, vol. 12, no. 3, pp. 49–69, Oct. 2010.