Conormal bundles to knots and the Gopakumar-Vafa conjecture

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dc.creatorKoshkin, Sergiy
dc.date2005-03-14
dc.date2007-03-20
dc.date.accessioned2026-07-07T07:52:33Z
dc.date.available2026-07-07T07:52:33Z
dc.descriptionWe offer a new construction of Lagrangian submanifolds for the Gopakumar-Vafa conjecture relating the Chern-Simons theory on the 3-sphere and the Gromov-Witten theory on the resolved conifold. Given a knot in the 3-sphere its conormal bundle is perturbed to disconnect it from the zero section and then pulled through the conifold transition. The construction produces totally real submanifolds of the resolved conifold that are Lagrangian in a perturbed symplectic structure and correspond to knots in a natural and explicit way. We prove that both the resolved conifold and the knot Lagrangians in it have bounded geometry, and that the moduli spaces of holomorphic curves ending on the Lagrangians are compact in the Gromov topology.
dc.descriptionProof of the main result simplified, conclusions and references added, exposition improved, typos fixed; 38 pages, 8 postscript figures
dc.identifierhttps://arxiv.org/abs/math/0503248
dc.identifierhttp://arxiv.org/abs/math/0503248
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125919
dc.subjectDifferential Geometry
dc.subjectHigh Energy Physics - Theory
dc.subjectSymplectic Geometry
dc.subject32Q65; 53D05; 53D12
dc.titleConormal bundles to knots and the Gopakumar-Vafa conjecture
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