Heegaard splittings of graph manifolds

Jennifer Schultens
2004 Geometry and Topology  
Let M be a totally orientable graph manifold with characteristic submanifold T and let M = V cup_S W be a Heegaard splitting. We prove that S is standard. In particular, S is the amalgamation of strongly irreducible Heegaard splittings. The splitting surfaces S_i of these strongly irreducible Heegaard splittings have the property that for each vertex manifold N of M, S_i cap N is either horizontal, pseudohorizontal, vertical or pseudovertical.
doi:10.2140/gt.2004.8.831 fatcat:bhwq4c5vebggte5dtvfcqkihji