Waldhausen's Theorem

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This note is an exposition of Waldhausen's proof of Waldhausen's Theorem: the three-sphere has a single Heegaard splitting, up to isotopy, in every genus. As a necessary step we also give a sketch of the Reidemeister-Singer Theorem.
This is the version published by Geometry & Topology Monographs on 3 December 2007

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