Lagrangians for the Gopakumar-Vafa conjecture

Abstract

This article explains how to construct immersed Lagrangian submanifolds in C^2 that are asymptotic at large distance from the origin to a given braid in the 3-sphere. The self-intersections of the Lagrangians are related to the crossings of the braid. These Lagrangians are then used to construct immersed Lagrangians in the vector bundle O(-1) oplus O(-1) over the Riemann sphere which are asymptotic at large distance from the zero section to braids.

This is the version published by Geometry & Topology Monographs on 22 April 2006

References in corpus (4)

• Disk Instantons, Mirror Symmetry and the Duality Web
• On Link Invariants and Topological String Amplitudes
• Enumerative geometry of stable maps with Lagrangian boundary conditions and multiple covers of the disc
• Open string instantons and relative stable morphisms

Cited by in corpus (3)

• Link Homologies and the Refined Topological Vertex
• Homological algebra of knots and BPS states
• Torus Knots in Lens Spaces & Topological Strings