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Classification of tight
contact structures on surgeries on the figure-eight knot
James Conway and Hyunki Min |
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Geometry & Topology 24 (2020) 1457–1517
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Abstract |
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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 –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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Keywords
contact geometry, contact structure, figure-eight knot,
surgery, tight, overtwisted
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Mathematical Subject Classification 2010
Primary: 57R17
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References |
Publication
Received: 13 February 2019
Revised: 29 August 2019
Accepted: 2 October 2019
Published: 30 September 2020
Proposed: András I Stipsicz
Seconded: Ciprian Manolescu, Ian Agol
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Authors |
| James Conway | |
| Department of Mathematics University of California, Berkeley Berkeley, CA United States |
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| Hyunki Min | |
| School of Mathematics Georgia Institute of Technology Atlanta, GA United States |
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