Klein bottle and toroidal Dehn fillings at distance 5

Sangyop Lee

Vol. 247 (2010), No. 2, 407–434

DOI: 10.2140/pjm.2010.247.407

Abstract

We determine all hyperbolic 3-manifolds M such that M(π) contains a Klein bottle, M(τ) contains an essential torus, and Δ(π,τ) = 5. As a corollary, we prove that if a hyperbolic 3-manifold M has two slopes π and τ on its boundary torus such that M(π) is a lens space containing a Klein bottle and M(τ) is toroidal, then Δ(π,τ) ≤ 4.

Keywords

toroidal manifolds, Klein bottles, Dehn fillings

Mathematical Subject Classification 2000

Primary: 57M50

Milestones

Received: 11 May 2009

Accepted: 14 June 2010

Published: 11 August 2010