Crossing number of links formed by edges of a triangulation

2001/10/17 by Simon A. King
Mathematics · #math.GT #msc:57M25 #msc:57Q15 #msc:52C45 #msc:52B22

paper · pdf

published as J. Knot Theory Ramifications 12 (2003) 281-286 · 4 pages

arxiv created 2001/10/17 · arxiv updated 2009/11/30

Abstract

We study the crossing number of links that are formed by edges of a triangulation T of the 3-sphere with n tetrahedra. We show that the crossing number is bounded from above by an exponential function of n². In general, this bound can not be replaced by a subexponential bound. However, if T is polytopal (resp. shellable) then there is a quadratic (resp. biquadratic) upper bound in n for the crossing number. In our proof, we use a numerical invariant p(T), called polytopality, that we have introduced in math.GT/0009216.

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