New York Journal of Mathematics
Volume 15 (2009) 1-17


Joseph D. Masters, William Menasco and Xingru Zhang

Heegaard splittings and virtually Haken Dehn filling. II

Published: January 22, 2009
Keywords: 3-manifolds, covering spaces, Heegaard splittings, knots, virually Haken
Subject: 57N10, 57M10; 58C40, 05C25, 57M15, 51M15

We use Heegaard splittings to give a criterion for a tunnel number one knot manifold to be nonfibered and to have large cyclic covers. We also show that a knot manifold satisfying the criterion admits infinitely many virtually Haken Dehn fillings. Using a computer, we apply this criterion to the 2 generator, nonfibered 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.


The second author was partially supported by NSF grant DMS 0306062. The third author was partially supported by NSF grant DMS 0204428.

Author information

Math Department, SUNY Buffalo