Reducing spheres and Klein bottles after Dehn fillings

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)265-267
Number of pages3
JournalCanadian Mathematical Bulletin
Issue number2
Publication statusPublished - 2003 Jun


  • Dehn filling
  • Klein bottle
  • Reducible

ASJC Scopus subject areas

  • General Mathematics


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