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

Conway, James¹ ; Min, Hyunki²

¹ Department of Mathematics, University of California, Berkeley, Berkeley, CA, United States
² School of Mathematics, Georgia Institute of Technology, Atlanta, GA, United States

Geometry & topology, Tome 24 (2020) no. 3, pp. 1457-1517.

Résumé

Two of the basic questions in contact topology are which manifolds admit tight contact structures, and on those that do, whether we can 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.

Détail

DOI : 10.2140/gt.2020.24.1457

Classification : 57R17
Keywords: contact geometry, contact structure, figure-eight knot, surgery, tight, overtwisted

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