Extension of Calabi homomorphism and non-simpleness of the area preserving homeomorphism group of $D^2$

Abstract

The content of this paper has no mathematical flaw except that the proof of the main theorem relies on the homotopy invariance of spectral invariants of topological Hamiltonian paths. Since the latter is still up in the air, the main result of the paper is the reduction of the extension problem of the Calabi homomorphism to the group of hameomorphism is still conjectural.

This paper is withdrawn by the author because the proof of homotopy invariance of spectral invariants of topological Hamiltonian paths provided in the paper arXiv1111.5992 contained a critical flaw, which is also withdrawn

References in corpus (3)

• On the uniqueness of generating Hamiltonian for continuous limits of Hamiltonians flows
• Homotopy invariance of spectral invariants of topological hamiltonian flows and its Lagrangian analog
• Simplicity of the group of compactly supported area preserving homeomorphisms of the open disc and fragmentation of symplectic diffeomorphisms

Cited by in corpus (1)

• Quasi-states, quasi-morphisms, and the moment map