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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