Inventiones mathematicae

, Volume 167, Issue 1, pp 135–177

Heegaard surfaces and measured laminations, I: The Waldhausen conjecture


DOI: 10.1007/s00222-006-0009-y

Cite this article as:
Li, T. Invent. math. (2007) 167: 135. doi:10.1007/s00222-006-0009-y


We give a proof of the so-called generalized Waldhausen conjecture, which says that an orientable irreducible atoroidal 3-manifold has only finitely many Heegaard splittings in each genus, up to isotopy. Jaco and Rubinstein have announced a proof of this conjecture using different methods.

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of MathematicsOklahoma State UniversityStillwaterUSA

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