Finite surgeries on three-tangle pretzel knots
Geometric Topology
2014-10-01 v2
Abstract
We classify Dehn surgeries on (p,q,r) pretzel knots that result in a manifold of finite fundamental group. The only hyperbolic pretzel knots that admit non-trivial finite surgeries are (-2,3,7) and (-2,3,9). Agol and Lackenby's 6-theorem reduces the argument to knots with small indices p,q,r. We treat these using the Culler-Shalen norm of the SL(2,C)-character variety. In particular, we introduce new techniques for demonstrating that boundary slopes are detected by the character variety.
Keywords
Cite
@article{arxiv.0809.4278,
title = {Finite surgeries on three-tangle pretzel knots},
author = {D. Futer and M. Ishikawa and Y. Kabaya and T. Mattman and K. Shimokawa},
journal= {arXiv preprint arXiv:0809.4278},
year = {2014}
}
Comments
18 pages, 15 figures v2 - minor revisions throughout