Another proof to Kotschick-Morita's Theorem of Kontsevich homomorphism

TL;DR

This paper provides a new proof of Kotschick and Morita's theorem on the decomposition of the Gel'fand-Kalinin-Fuks class using Gr"obner Basis theory and computer algebra, confirming the isomorphism of a specific Kontsevich homomorphism.

Contribution

The paper introduces a novel proof of a known theorem on Kontsevich homomorphism utilizing computational algebra techniques.

Findings

Confirmed the decomposition of the Gel'fand-Kalinin-Fuks class.

Validated the isomorphism of the Kontsevich homomorphism.

Demonstrated the effectiveness of Gr"obner Basis methods in this context.

Abstract

In \cite{KOT:MORITA}, Kotschick and Morita showed that the Gel'fand-Kalinin-Fuks class in $\ds \HGF{7}{2}{}{8}$ is decomposed as a product $\eta\wedge \omega $ of some leaf cohomology class $\eta$ and a transverse symplectic class $\omega$. In other words, the Kontsevich homomorphism $\ds\omega\wedge :\HGF{5}{2}{0}{10} \rightarrow\HGF{7}{2}{}{8}$ is isomorphic. In this paper, we give proof for the Kotschick and Morita's theorem by using the Gr\"obner Basis theory and computer symbol calculations.