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- W4299559636 abstract "Haken showed that the Heegaard splittings of reducible 3-manifolds are reducible, that is, a reducing 2-sphere can be found which intersects the Heegaard surface in a single simple closed curve. When the genus of the interesting surface increases from zero, more complicated phenomena occur. Kobayashi showed that if a 3-manifold $M^3$ contains an essential torus $T$, then it contains one which can be isotoped to intersect a strongly irreducible Heegaard splitting surface $F$ in a collection of simple closed curves which are essential in $T$ and in $F$. In general there is no global bound on the number of curves in this collection. We give conditions under which a global bound can be obtained." @default.
- W4299559636 created "2022-10-02" @default.
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- W4299559636 date "2016-03-26" @default.
- W4299559636 modified "2023-09-30" @default.
- W4299559636 title "Tori and Heegaard splittings" @default.
- W4299559636 doi "https://doi.org/10.48550/arxiv.1603.08154" @default.
- W4299559636 hasPublicationYear "2016" @default.
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