Algebraic and Geometric Topology 1 (2001),
paper no. 38, pages 763-790.
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, i.e. admits a Heegaard splitting obtained
by attaching a single 1-handle to one or two components of boundary
M_i. This result also holds for a decomposition of M along a maximal
collection of incompressible tori.
3-manifold, Heegaard splitting, incompressible surface
AMS subject classification.
Submitted: 18 April 2001.
(Revised: 27 July 2001.)
Accepted: 3 October 2001.
Published: 11 December 2001.
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