Inventiones mathematicae

, Volume 167, Issue 1, pp 135-177

First online:

Heegaard surfaces and measured laminations, I: The Waldhausen conjecture

  • Tao LiAffiliated withDepartment of Mathematics, Oklahoma State University Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.