Decomposing Heegaard splittings along separating incompressible surfaces in 3-manifolds

Kazuhiro Ichihara; Makoto Ozawa; J. Hyam Rubinstein

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arXiv · 1803.09023

Decomposing Heegaard splittings along separating incompressible surfaces in 3-manifolds

Kazuhiro Ichihara·Makoto Ozawa·J. Hyam Rubinstein

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Abstract

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.

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Kazuhiro Ichihara, Makoto Ozawa, J. Hyam Rubinstein. 2018-03-24. Decomposing Heegaard splittings along separating incompressible surfaces in 3-manifolds. https://arxiv.org/abs/1803.09023

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