Vol. 247, No. 2, 2010

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ISSN: 0030-8730
Klein bottle and toroidal Dehn fillings at distance 5

Sangyop Lee

Vol. 247 (2010), No. 2, 407–434
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
Authors
Sangyop Lee
Department of Mathematics
Chung-Ang University
221 Heukseok-dong, Dongjak-gu
Seoul 156-756
South Korea