English

Annular and boundary reducing Dehn fillings

Geometric Topology 2007-05-23 v1

Abstract

A manifold M is simple if it contains no essential disk, sphere, annulus or torus. If M is simple and two Dehn fillings M(r_1), M(r_2) are nonsimple, then there is an upper bound on \Delta(r_1,r_2), the geometric intersection number between r_1 and r_2. There are 10 possibilities, depending on the types of M(r_i). In this paper it will be shown that if M(r_1) contains an essential disk and M(r_2) contains an essential annulus, then \Delta(r_1,r_2) is at most two. This completes the determination of the best possible upper bounds on \Delta(r_1, r_2) for all ten cases.

Keywords

Cite

@article{arxiv.math/9810126,
  title  = {Annular and boundary reducing Dehn fillings},
  author = {Cameron McA. Gordon and Ying-Qing Wu},
  journal= {arXiv preprint arXiv:math/9810126},
  year   = {2007}
}

Comments

23 pages, 7 figures

R2 v1 2026-07-22T18:00:33.518Z