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

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

2005-07-14

arxiv.org/abs/math/0507294v1

Algebr. Geom. Topol. 5 (2005) 563-576

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-24.abs.html

Scientific paper

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.

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