Mathematics – Geometric Topology
Scientific paper
1998-11-06
Algebr. Geom. Topol. 1 (2001) 763-790
Mathematics
Geometric Topology
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-38.abs.html
Scientific paper
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.
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