Lagrangians for the Gopakumar-Vafa conjecture

Details Lagrangians for the Gopakumar-Vafa conjecture Lagrangians for the Gopakumar-Vafa conjecture

2002-01-22

arxiv.org/abs/math/0201219v2

Geom. Topol. Monogr. 8 (2006) 73-95

Mathematics

Differential Geometry

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

Scientific paper

10.2140/gtm.2006.8.73

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.

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