Multiple genus 2 Heegaard splittings: a missed case

Berge, John; Scharlemann, Martin

doi:10.2140/agt.2011.11.1781

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Multiple genus 2 Heegaard splittings: a missed case

John Berge and Martin Scharlemann

Algebraic & Geometric Topology 11 (2011) 1781–1792

DOI: 10.2140/agt.2011.11.1781

Abstract

A gap in [H Rubinstein, M Scharlemann, Genus two Heegaard splittings of orientable 3–manifolds, in “Proceedings of the Kirbyfest”, Geom. Topol. Monogr. 2 (1999) 489–553] is explored: new examples are found of closed orientable 3–manifolds with possibly multiple genus 2 Heegaard splittings. Properties common to all the examples in that paper are not universally shared by the new examples: some of the new examples have Hempel distance 3, and it is not clear that a single stabilization always makes the multiple splittings isotopic.

Keywords

Heegaard splittings, Hempel distance

Mathematical Subject Classification 2000

Primary: 57M15, 57N10

References

Publication

Received: 10 May 2010

Revised: 11 April 2011

Accepted: 13 April 2011

Published: 3 June 2011

Authors

John Berge
Independent Madison 53711 Wisconsin USA

Martin Scharlemann
Department of Mathematics University of California Santa Barbara CA 93106 USA

Volume 11, issue 3 (2011)