Exceptional surgery on knots
Abstract
Let be an irreducible, compact, connected, orientable 3-manifold whose boundary is a torus. We show that if is hyperbolic, then it admits at most six finite/cyclic fillings of maximal distance 5. Further, the distance of a finite/cyclic filling to a cyclic filling is at most 2. If has a non-boundary-parallel, incompressible torus and is not a generalized 1-iterated torus knot complement, then there are at most three finite/cyclic fillings of maximal distance 1. Further, if has a non-boundary-parallel, incompressible torus and is not a generalized 1- or 2-iterated torus knot complement and if admits a cyclic filling of odd order, then does not admit any other finite/cyclic filling. Relations between finite/cyclic fillings and other exceptional fillings are also discussed.
Cite
@article{arxiv.math/9410215,
title = {Exceptional surgery on knots},
author = {Steven Boyer and Xingru Zhang},
journal= {arXiv preprint arXiv:math/9410215},
year = {2016}
}
Comments
7 pages