Heegaard splittings and virtually Haken Dehn filling II

2006/12/07 by Joseph D. Masters, Masters, Joseph D., William W. Menasco +3
Mathematics · #57M10 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0612199

openalex publication_date 2006/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Dehn Surgery on Knots
• Heegaard splittings, the virtually Haken conjecture and Property tau

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