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Abstract
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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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Keywords
hyperbolic flows, templates, prime knots, composite knots,
positive braids
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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
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