Volume 5, issue 2 (2005)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Knots on a positive template have a bounded number of prime factors

Michael C Sullivan

Algebraic & Geometric Topology 5 (2005) 563–576

arXiv: math.GT/0507294

Abstract

Templates are branched 2–manifolds with semi-flows used to model “chaotic” hyperbolic invariant sets of flows on 3–manifolds. Knotted orbits on a template correspond to those in the original flow. Birman and Williams conjectured that for any given template the number of prime factors of the knots realized would be bounded. We prove a special case when the template is positive; the general case is now known to be false.

Keywords
hyperbolic flows, templates, prime knots, composite knots, positive braids
Mathematical Subject Classification 2000
Primary: 37D45
Secondary: 57M25
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Publication
Received: 1 February 2005
Accepted: 31 May 2005
Published: 29 June 2005
Authors
Michael C Sullivan
Department of Mathematics (4408)
Southern Illinois University
Carbondale IL 62901
USA
http://www.math.siu.edu/sullivan/