Volume 6 (2006)
Download this article
For screen
For printing
Recent Issues

Volume 13 (2013)
Issue 1 1–624
Issue 2 625–1241
Issue 3 1243–1856
Issue 4 1857–

Volume 12 (2012) 1–4

Volume 11 (2011) 1–5

Volume 10 (2010) 1–4

Volume 9 (2009) 1–4

Volume 8 (2008) 1–4

Volume 7 (2007)

Volume 6 (2006)

Volume 5 (2005)

Volume 4 (2004)

Volume 3 (2003)

Volume 2 (2002)

Volume 1 (2001)
The Journal
About the Journal
Editorial Board
Editorial Interests
Author Index
Editorial procedure
Submission Guidelines
Submission Page
Author copyright form
Subscriptions
Contacts
G&T Publications
GTP Author Index

The diameter of the set of boundary slopes of a knot

Ben Klaff and Peter B Shalen

Algebraic & Geometric Topology 6 (2006) 1095–1112

DOI: 10.2140/agt.2006.6.1095

arXiv: math.GT/0412147
Abstract

Let K be a tame knot with irreducible exterior M(K) in a closed, connected, orientable 3–manifold Σ such that π1(Σ) is cyclic. If ∞ is not a strict boundary slope, then the diameter of the set of strict boundary slopes of K, denoted dK, is a numerical invariant of K. We show that either (i) dK≥2 or (ii) K is a generalized iterated torus knot. The proof combines results from Culler and Shalen [Comment. Math. Helv. 74 (1999) 530–547] with a result about the effect of cabling on boundary slopes.

Keywords

knot exterior, strict essential surface, strict boundary slope, diameter, 3–manifold, cyclic fundamental group, cable knot, generalized iterated torus knot
Mathematical Subject Classification

Primary: 57M15, 57M25

Secondary: 57M50
References
Forward citations
Publication

Received: 12 November 2005
Accepted: 14 March 2006
Published: 29 August 2006
Authors
Ben Klaff
Department of Mathematics
University of Texas at Austin
1 University Station
Austin, TX 78741
USA
Peter B Shalen
Department of Mathematics, Statistics, and Computer Science (M/C 249)
University of Illinois at Chicago
851 S. Morgan St.
Chicago, IL 60607-7045
USA