Volume 7, issue 1 (2007)

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

Volume 18
Issue 4, 1883–2507
Issue 3, 1259–1881
Issue 2, 635–1258
Issue 1, 1–633

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Volumes of highly twisted knots and links

Jessica S Purcell

Algebraic & Geometric Topology 7 (2007) 93–108

arXiv: math.GT/0604476

Abstract

We show that for a large class of knots and links with complements in S3 admitting a hyperbolic structure, we can determine bounds on the volume of the link complement from combinatorial information given by a link diagram. Specifically, there is a universal constant C such that if a knot or link admits a prime, twist reduced diagram with at least 2 twist regions and at least C crossings per twist region, then the link complement is hyperbolic with volume bounded below by 3.3515 times the number of twist regions in the diagram. C is at most 113.

Keywords
hyperbolic knot complements, hyperbolic link complements, volume, cone manifolds
Mathematical Subject Classification 2000
Primary: 57M25, 57M50
References
Publication
Received: 21 April 2006
Revised: 3 January 2007
Accepted: 3 January 2007
Published: 23 February 2007
Authors
Jessica S Purcell
Department of Mathematics
1 University Station C1200
University of Texas at Austin
Austin, TX 78712