The Lie algebra of the fundamental group of a surface as a symplectic module

TL;DR

This paper derives a formula characterizing the Lie algebra of a surface's fundamental group as a symplectic module, enhancing understanding of its algebraic structure in relation to surface topology.

Contribution

It introduces a explicit formula for the character of the Lie algebra as a symplectic module, linking algebraic and topological properties of surfaces.

Findings

Derived a formula for the character of the Lie algebra as a symplectic module

Established connections between surface topology and algebraic representations

Provided tools for further algebraic analysis of surface groups

Abstract

This note provides a formula for the character of the Lie algebra of the fundamental group of a surface, viewed as a module over the symplectic group.