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Classification of tight contact structures on surgeries on the figure-eight knot

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arxiv 1901.06066 v2 pith:5K4QBJQ7 submitted 2019-01-18 math.GT math.SG

James Conway , Hyunki Min This is my paper · ORCID
classification math.GTmath.SG
keywords contactstructurestightclassificationfigure-eightknotmanifoldssurgeries
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Two of the basic questions in contact topology are which manifolds admit tight contact structures, and on those that do, can we classify such structures. We present the first such classification on an infinite family of (mostly) hyperbolic 3-manifolds: surgeries on the figure-eight knot. We also determine which of the tight contact structures are symplectically fillable and which are universally tight.

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