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# Reducing Spheres and Klein Bottles after Dehn Fillings

Published:2003-06-01
Printed: Jun 2003
• Seungsang Oh
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## Abstract

Let $M$ be a compact, connected, orientable, irreducible 3-manifold with a torus boundary. It is known that if two Dehn fillings on $M$ along the boundary produce a reducible manifold and a manifold containing a Klein bottle, then the distance between the filling slopes is at most three. This paper gives a remarkably short proof of this result.
 Keywords: Dehn filling, reducible, Klein bottle
 MSC Classifications: 57M50 - Geometric structures on low-dimensional manifolds