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Klein slopes on hyperbolic 3-manifolds

Published online by Cambridge University Press:  01 September 2007

DANIEL MATIGNON  and
NABIL SAYARI
DANIEL MATIGNON
Affiliation:
C.M.I. Université de Provence, 39 rue Joliot Curie, 13453 Marseille, Cedex 13, France. email: matignon@cmi.univ-mrs.fr
NABIL SAYARI
Affiliation:
Département de Mathématiques et de Statistique, Université de Moncton, NB, Canada. email: sayarin@umoncton.ca
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Abstract

This paper is devoted to 3-manifolds which admit two distinct Dehn fillings producing a Klein bottle.

Let M be a compact, connected and orientable 3-manifold whose boundary contains a 2-torus T. If M is hyperbolic then only finitely many Dehn fillings along T yield non-hyperbolic manifolds. We consider the situation where two distinct slopes γ1, γ2 produce a Klein bottle. We give an upper bound for the distance Δ(γ1, γ2), between γ1 and γ2. We show that there are exactly four hyperbolic manifolds for which Δ(γ1, γ2) > 4.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 2 , September 2007 , pp. 419 - 447
Copyright
Copyright © Cambridge Philosophical Society 2007

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