The $L_\infty$-algebra of a symplectic manifold

TL;DR

This paper constructs an $L_ abla$-algebra on the canonical homology complex of a symplectic manifold, linking it to the universal central extension of Hamiltonian vector fields' Lie algebra.

Contribution

It introduces a novel $L_ abla$-algebra structure on the homology complex that connects to fundamental symplectic and Hamiltonian algebraic structures.

Findings

Defines an $L_ abla$-algebra on the truncated canonical homology complex.

Establishes a natural projection to the universal central extension of Hamiltonian vector fields.

Provides a new algebraic framework for symplectic geometry.

Abstract

We construct an $L_\infty$-algebra on the truncated canonical homology complex of a symplectic manifold, which naturally projects to the universal central extension of the Lie algebra of Hamiltonian vector fields.