2018年3月24日
Decomposing Heegaard splittings along separating incompressible surfaces in 3-manifolds
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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.
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.
- リンク情報
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- arXiv
- http://arxiv.org/abs/arXiv:1803.09023
- Arxiv Url
- http://arxiv.org/abs/1803.09023v1
- Arxiv Url
- http://arxiv.org/pdf/1803.09023v1 本文へのリンクあり
- ID情報
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- arXiv ID : arXiv:1803.09023