Cusp shape and tunnel number
Geometric Topology
2018-07-26 v2
Abstract
We show that the set of cusp shapes of hyperbolic tunnel number one manifolds is dense in the Teichmuller space of the torus. A similar result holds for tunnel number n manifolds. As a consequence, for fixed n, there are infinitely many hyperbolic tunnel number n manifolds with at most one exceptional Dehn filling. This is in contrast to large volume Berge knots, which are tunnel number one manifolds, but with cusp shapes converging to a single point in Teichmuller space.
Cite
@article{arxiv.1711.03693,
title = {Cusp shape and tunnel number},
author = {Vinh Dang and Jessica S. Purcell},
journal= {arXiv preprint arXiv:1711.03693},
year = {2018}
}
Comments
15 pages, 6 figures. V2: Examples and references have been added, additional references updated