Lagrangians for the Gopakumar-Vafa conjecture
Clifford Henry Taubes
Abstract
This article explains how to construct immersed Lagrangian submanifolds in C2 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.
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