Bouchard-Klemm-Marino-Pasquetti Conjecture for $\mathbb{C}^3$

TL;DR

This paper proves the Bouchard-Klemm-Marino-Pasquetti conjecture for the framed vertex in topological string theory using the symmetrized Cut-Join Equation, advancing understanding of enumerative geometry and string dualities.

Contribution

It provides the first proof of the conjecture for the framed vertex leveraging the symmetrized Cut-Join Equation, connecting combinatorial and geometric methods.

Findings

Confirmed the conjecture for the framed vertex case.

Established a new application of the symmetrized Cut-Join Equation.

Enhanced the mathematical understanding of topological string invariants.

Abstract

In this paper, we give a proof of the Bouchard-Klemm-Marino-Pasquetti conjecture for a framed vertex, by using the symmetrized Cut-Join Equation developed in a previous paper.