Lagrangians for the Gopakumar-Vafa conjecture

Clifford Henry Taubes

Lagrangians for the Gopakumar-Vafa conjecture

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arxiv math/0201219 v2 pith:Q7PCURY7 submitted 2002-01-22 math.DG math-phmath.GTmath.MP

Clifford Henry Taubes This is my paper · ORCID

classification math.DGmath-phmath.GTmath.MP

keywords lagrangiansasymptoticbraidconstructdistanceimmersedlargesphere

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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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