Heegaard splittings and virtually Haken Dehn filling II

Details Heegaard splittings and virtually Haken Dehn filling II Heegaard splittings and virtually Haken Dehn filling II

2006-12-07

arxiv.org/abs/math/0612199v2

Mathematics

Geometric Topology

17 pages, 1 figure, 1 table

Scientific paper

We use Heegaard splittings to give a criterion for a tunnel number one knot manifold to be non-fibered and to have large cyclic covers. We also show that such a knot manifold (satisfying the criterion) admits infinitely many virtually Haken Dehn fillings. Using a computer, we apply this criterion to the 2 generator, non-fibered knot manifolds in the cusped Snappea census. For each such manifold M, we compute a number c(M), such that, for any n>c(M), the n-fold cyclic cover of M is large.

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