2018/03/24 by Ichihara, Kazuhiro, Ozawa, Makoto, Rubinstein, J. Hyam
#FOS: Mathematics #Geometric Topology (math.GT) #Primary 57M50. Secondary 57N10
paper · doi:10.48550/arxiv.1803.09023
In this paper, by putting a separating incompressible surface in a 3-manifold into Morse position relative to the height function associated to a strongly irreducible Heegaard splitting, we show that an incompressible subsurface of the Heegaard splitting can be found, by decomposing the 3-manifold along the separating surface. Further if the Heegaard surface is of Hempel distance at least 4, then there is a pair of such subsurfaces on both sides of the given separating surface. This gives a particularly simple hierarchy for the 3-manifold.