%0 Journal Article
%T Genus two 3-manifolds are built from handle number one pieces
%A Eric Sedgwick
%J Mathematics
%D 1998
%I arXiv
%R 10.2140/agt.2001.1.763
%X 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.
%U http://arxiv.org/abs/math/9811029v2