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.