Volume 24, issue 3 (2020)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 3, 1075–1614
Issue 2, 533–1073
Issue 1, 1–532

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Classification of tight contact structures on surgeries on the figure-eight knot

James Conway and Hyunki Min

Geometry & Topology 24 (2020) 1457–1517
Abstract

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.

Keywords
contact geometry, contact structure, figure-eight knot, surgery, tight, overtwisted
Mathematical Subject Classification 2010
Primary: 57R17
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
Authors
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