One-sided Heegaard splittings of ℝP3

Bartolini, Loretta; Rubinstein, J Hyam

doi:10.2140/agt.2006.6.1319

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One-sided Heegaard splittings of $\mathbb{R}\mathrm{P}^3$

Loretta Bartolini and J Hyam Rubinstein

Algebraic & Geometric Topology 6 (2006) 1319–1330

DOI: 10.2140/agt.2006.6.1319

arXiv: math.GT/0509007

Abstract

Using basic properties of one-sided Heegaard splittings, a direct proof that geometrically compressible one-sided splittings of $ℝ P^{3}$ are stabilised is given. The argument is modelled on that used by Waldhausen to show that two-sided splittings of $S^{3}$ 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

Volume 6, issue 3 (2006)