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Heegaard splittings and virtually Haken Dehn filling II

Joseph D. Masters·William Menasco·Xingru Zhang
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Abstract

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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Joseph D. Masters, William Menasco, Xingru Zhang. 2006-12-07. Heegaard splittings and virtually Haken Dehn filling II. https://arxiv.org/abs/math/0612199

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