Volume 21, issue 7 (2021)

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

Volume 22, 1 issue

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Turaev hyperbolicity of classical and virtual knots

Colin Adams, Or Eisenberg, Jonah Greenberg, Kabir Kapoor, Zhen Liang, Kate O’Connor, Natalia Pachecho-Tallaj and Yi Wang

Algebraic & Geometric Topology 21 (2021) 3459–3482
Abstract

By work of W Thurston, knots and links in the 3–sphere are known to either be torus links; or to contain an essential sphere or torus in their complement; or to be hyperbolic, in which case a unique hyperbolic volume can be calculated for their complement. We employ a construction of Turaev to associate a family of hyperbolic 3–manifolds of finite volume to any classical or virtual link, even if nonhyperbolic. These are in turn used to define the Turaev volume of a link, which is the minimal volume among all the hyperbolic 3–manifolds associated via this Turaev construction. In the case of a classical link, we can also define the classical Turaev volume, which is the minimal volume among all the hyperbolic 3–manifolds associated via this Turaev construction for the classical projections only. We then investigate these new invariants.

Keywords
Turaev surface, Turaev volume, knot, hyperbolic knot, virtual knot
Mathematical Subject Classification
Primary: 57K10, 57K32
References
Publication
Received: 31 March 2020
Revised: 26 October 2020
Accepted: 9 November 2020
Published: 28 December 2021
Authors
Colin Adams
Department of Mathematics
Williams College
Williamstown, MA
United States
Or Eisenberg
Boulder, CO
United States
Jonah Greenberg
New York, NY
United States
Kabir Kapoor
Department of Mathematics
University of California, Berkeley
Berkeley, CA
United States
Zhen Liang
Department of Mathematics
Boston College
Chestnut Hill, MA
United States
Kate O’Connor
Department of Mathematics
Rice University
Houston, TX
United States
Natalia Pachecho-Tallaj
Department of Mathematics
MIT
Cambridge, MA
United States
Yi Wang
Department of Mathematics
University of Pennsylvania
Philadelphia, PA
United States