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arXiv:math/0110174 [math.GT]AbstractReferencesReviewsResources

Crossing number of links formed by edges of a triangulation

Simon A. King

Published 2001-10-17Version 1

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 n^2. 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.

Comments: 4 pages
Journal: J. Knot Theory Ramifications 12 (2003) 281-286
Categories: math.GT
Subjects: 57M25, 57Q15, 52C45, 52B22
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