Genus two 3-manifolds are built from handle number one pieces
Geometric Topology
2014-10-01 v2
Abstract
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.
Cite
@article{arxiv.math/9811029,
title = {Genus two 3-manifolds are built from handle number one pieces},
author = {Eric Sedgwick},
journal= {arXiv preprint arXiv:math/9811029},
year = {2014}
}
Comments
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-38.abs.html