Communications in Analysis and Geometry

Volume 14 (2006)

Number 2

Heegaard splittings of the form $H+nK$

Pages: 215 – 247



Yoav Moriah

Saul Schleimer

Eric Sedgwick


Suppose that a three-manifold $M$ contains infinitely many distinct strongly irreducible Heegaard splittings $H+nK$, obtained by Haken summing the surface $H$ with $n$ copies of the surface $K$. We show that $K$ is incompressible. All known examples, of manifolds containing infinitely many irreducible Heegaard splittings, are of this form. We also give new examples of such manifolds.

2010 Mathematics Subject Classification

Primary 57N10. Secondary 57M25.

Published 1 January 2006