Heegaard surfaces and measured laminations, I: The Waldhausen conjecture
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- Li, T. Invent. math. (2007) 167: 135. doi:10.1007/s00222-006-0009-y
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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.