Volume 12 (2007)

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Waldhausen's Theorem

Saul Schleimer

Geometry & Topology Monographs 12 (2007) 299–317

DOI: 10.2140/gtm.2007.12.299

arXiv: 0904.0182

Abstract

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.

Keywords

triangulations of three-manifolds, Heegaard splittings, stabilization, three-sphere

Mathematical Subject Classification

Primary: 57M40, 57N10

Secondary: 57Q15

References
Publication

Received: 16 January 2007
Revised: 1 October 2007
Accepted: 6 November 2007
Published: 3 December 2007

Authors
Saul Schleimer
Department of Mathematics
University of Warwick
Coventry, CV4 7AL
UK