About the x-y symmetry of the F_g algebraic invariants

TL;DR

This paper completes the proof of the x-y symmetry property of symplectic invariants, clarifying previous proofs and including missing integration constants to solidify the result.

Contribution

It provides a complete proof of the x-y symmetry of symplectic invariants, addressing gaps and missing constants in prior work.

Findings

Confirmed the x-y symmetry of symplectic invariants.

Included integration constants previously omitted.

Strengthened the theoretical foundation of symplectic invariants.

Abstract

We complete the proof of the x-y symmetry of symplectic invariants of [EO]. We recall the main steps of the proof of [EO2], and we include the integration constants absent in [EO2].