Reducing Spheres and Klein Bottles after Dehn Fillings

[摘要] Let $M$ be a compact, connected, orientable, irreducible 3-manifold with atorus boundary. It is known that if two Dehn fillings on $M$ along theboundary produce a reducible manifold and a manifold containing a Kleinbottle, then the distance between the filling slopes is at most three. Thispaper gives a remarkably short proof of this result.

[学科分类] 数学（综合）

[关键词] Dehn filling;reducible;Klein bottle