Volume 2, issue 1 (1998)

Download this article
For printing
Recent Issues

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

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
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A natural framing of knots

Michael T Greene and Bert Wiest

Geometry & Topology 2 (1998) 31–64

arXiv: math.GT/9803168

Abstract

Given a knot K in the 3–sphere, consider a singular disk bounded by K and the intersections of K with the interior of the disk. The absolute number of intersections, minimised over all choices of singular disk with a given algebraic number of intersections, defines the framing function of the knot. We show that the framing function is symmetric except at a finite number of points. The symmetry axis is a new knot invariant, called the natural framing of the knot. We calculate the natural framing of torus knots and some other knots, and discuss some of its properties and its relations to the signature and other well-known knot invariants.

Keywords
knot, link, knot invariant, framing, natural framing, torus knot, Cayley graph
Mathematical Subject Classification
Primary: 57M25
Secondary: 20F05
References
Forward citations
Publication
Received: 4 August 1997
Accepted: 19 March 1998
Published: 21 March 1998
Proposed: Cameron Gordon
Seconded: Joan Birman, Walter Neumann
Authors
Michael T Greene
Mathematics Institute
University of Warwick
Coventry
CV4 7AL
United Kingdom
Bert Wiest
Mathematics Institute
University of Warwick
Coventry
CV4 7AL
United Kingdom