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math.GT1998
The structure of a solvmanifold's Heegaard splittings
Daryl Cooper, Martin Scharlemann
We classify isotopy classes of irreducible Heegaard splittings of solvmanifolds. If the monodromy of the solvmanifold can be expressed as a 2 x 2 matrix with 0 in the lower right h…
math.GT1998
Comparing Heegaard and JSJ structures of orientable 3-manifolds
Martin Scharlemann, Jennifer Schultens
The Heegaard genus g of an irreducible closed orientable 3-manifold puts a limit on the number and complexity of the pieces that arise in the Jaco-Shalen-Johannson decomposition of…