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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
One-sided Heegaard splittings of $\mathbb{R}\mathrm{P}^3$

Loretta Bartolini and J Hyam Rubinstein

Algebraic & Geometric Topology 6 (2006) 1319–1330

arXiv: math.GT/0509007

Abstract

Using basic properties of one-sided Heegaard splittings, a direct proof that geometrically compressible one-sided splittings of P3 are stabilised is given. The argument is modelled on that used by Waldhausen to show that two-sided splittings of S3 are standard.

Keywords
one-sided Heegaard splitting, geometrically compressible
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57N10
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Publication
Received: 31 August 2005
Revised: 6 July 2006
Accepted: 20 July 2006
Published: 20 September 2006
Authors
Loretta Bartolini
Department of Mathematics and Statistics
University of Melbourne
Parkville VIC 3010
Australia
J Hyam Rubinstein
Department of Mathematics and Statistics
University of Melbourne
Parkville VIC 3010
Australia