Topological extension of Calabi homomorphism and non-simpleness of the area-preserving homeomorphism group of two-disc

TL;DR

This paper discusses a topological extension of the Calabi homomorphism and explores the non-simpleness of the area-preserving homeomorphism group of a two-disc, despite noting a significant mistake in the original argument.

Contribution

It attempts to extend the Calabi homomorphism topologically and analyze the algebraic structure of the area-preserving homeomorphism group of a two-disc.

Findings

Identification of a mistake in the original proof

Implication that the transfer map's effect is nullified

Discussion on the non-simpleness of the group

Abstract

The paper contains a silly mistake in the usage of the equation (5.4) in the formula (6.5). Due to this mistake, the effect of the transfer map $phi$ is nullified. I am deeply sorry for not being very careful in my submission and making this mistake.