Algebraic and Geometric Topology 5 (2005), paper no. 24, pages 563-576.

Knots on a positive template have a bounded number of prime factors

Michael C. Sullivan

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

AMS subject classification. Primary: 37D45. Secondary: 57M25.

E-print: arXiv:math.GT/0507294

DOI: 10.2140/agt.2005.5.563

Submitted: 1 February 2005. Accepted: 31 May 2005. Published: 29 June 2005.

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Michael C. Sullivan
Department of Mathematics (4408), Southern Illinois University
Carbondale, IL 62901, USA
Email: msulliva@math.siu.edu
URL: http://www.math.siu.edu/sullivan

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