Genus two 3–manifolds are built from handle number one pieces

Let $M$ be a closed, irreducible, genus two 3–manifold, and $F$ a maximal collection of pairwise disjoint, closed, orientable, incompressible surfaces embedded in $M$ . Then each component manifold $M_{i}$ of $M - F$ has handle number at most one, ie admits a Heegaard splitting obtained by attaching a single 1–handle to one or two components of $\partial M_{i}$ . This result also holds for a decomposition of $M$ along a maximal collection of incompressible tori.

Keywords

3–manifold, Heegaard splitting, incompressible surface

Mathematical Subject Classification 2000

Primary: 57M99

References

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Publication

Received: 18 April 2001

Revised: 27 July 2001

Accepted: 3 October 2001

Published: 11 December 2001

Authors

Eric Sedgwick
DePaul University Department of Computer Science 243 S Wabash Ave Chicago IL 60604 USA

Volume 1, issue 2 (2001)

Eric Sedgwick