Volumes of highly twisted knots and links

Purcell, Jessica

doi:10.2140/agt.2007.7.93

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Volumes of highly twisted knots and links

Jessica S Purcell

Algebraic & Geometric Topology 7 (2007) 93–108

DOI: 10.2140/agt.2007.7.93

arXiv: math.GT/0604476

Abstract

We show that for a large class of knots and links with complements in $S^{3}$ 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

Volume 7, issue 1 (2007)