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

James Conway and Hyunki Min

Geometry & Topology 24 (2020) 1457–1517

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.

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contact geometry, contact structure, figure-eight knot, surgery, tight, overtwisted
Mathematical Subject Classification 2010
Primary: 57R17
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
James Conway
Department of Mathematics
University of California, Berkeley
Berkeley, CA
United States
Hyunki Min
School of Mathematics
Georgia Institute of Technology
Atlanta, GA
United States