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

TL;DR

This paper explores the extension of the Calabi homomorphism and discusses the non-simpleness of the area-preserving homeomorphism group of the disk, highlighting conjectural aspects related to spectral invariants.

Contribution

It reduces the problem of extending the Calabi homomorphism to the group of hameomorphisms, connecting it to spectral invariants conjecturally.

Findings

Main theorem's proof depends on unproven homotopy invariance of spectral invariants.

Reduction of the extension problem to hameomorphism group.

Highlights conjectural status of the main results.

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.