show/hide this revision's text 2 rephrased definition of n

Lower bound on # number of tetrahedra needed to triangulate a knot complement

Following along a similar line to the question asked here: http://mathoverflow.net/questions/38082/is-there-an-explicit-bound-on-the-number-of-tetrahedra-needed-to-triangulate-a-hy

Let $K$ be a (hyperbolic) knot in $S^3$ with S^3$. Let $n$ be the minimal number of crossings of any diagram of $K$ and let $M = S^3 \backslash K$ be its complement. By Moise’s theorem the 3-manifold $M$ can be triangulated by tetrahedra. But is there any known bound on the number of tetrahedra needed to triangulate $M$ as a function of $n$? I am particularly interested in any known lower bounds, but upper bounds would also be interesting.
show/hide this revision's text 1

Lower bound on # tetrahedra needed to triangulate a knot complement

Following along a similar line to the question asked here: http://mathoverflow.net/questions/38082/is-there-an-explicit-bound-on-the-number-of-tetrahedra-needed-to-triangulate-a-hy

Let $K$ be a (hyperbolic) knot in $S^3$ with $n$ crossings and let $M = S^3 \backslash K$ be its complement. By Moise’s theorem the 3-manifold $M$ can be triangulated by tetrahedra. But is there any known bound on the number of tetrahedra needed to triangulate $M$ as a function of $n$? I am particularly interested in any known lower bounds, but upper bounds would also be interesting.