Non-parallel essential surfaces in knot complements

Details Non-parallel essential surfaces in knot complements Non-parallel essential surfaces in knot complements

2003-02-22

arxiv.org/abs/math/0302272v2

Mathematics

Geometric Topology

10 pages, 4 figures. Revised version

Scientific paper

We show that if a knot or link has n thin levels when put in thin position
then its exterior contains a collection of n disjoint, non-parallel, planar,
meridional, essential surfaces. A corollary is that there are at least n/3
tetrahedra in any triangulation of the complement of such a knot.

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