Crossing number of links formed by edges of a triangulation
Geometric Topology
2007-05-23 v1
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 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.
Cite
@article{arxiv.math/0110174,
title = {Crossing number of links formed by edges of a triangulation},
author = {Simon A. King},
journal= {arXiv preprint arXiv:math/0110174},
year = {2007}
}
Comments
4 pages