English

Exceptional surgery on knots

Geometric Topology 2016-09-06 v1

Abstract

Let MM be an irreducible, compact, connected, orientable 3-manifold whose boundary is a torus. We show that if MM 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 MM 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 MM has a non-boundary-parallel, incompressible torus and is not a generalized 1- or 2-iterated torus knot complement and if MM admits a cyclic filling of odd order, then MM does not admit any other finite/cyclic filling. Relations between finite/cyclic fillings and other exceptional fillings are also discussed.

Keywords

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