Geodesic
Saddle tangencies and the distance of Heegaard splittings
Li, Tao1
1Department of Mathematics, Boston College, Chestnut Hill, MA 02467, USA
Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 1119-1134
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We give another proof of a theorem of Scharlemann and Tomova and of a theorem of Hartshorn. The two theorems together say the following. Let M be a compact orientable irreducible 3–manifold and P a Heegaard surface of M. Suppose Q is either an incompressible surface or a strongly irreducible Heegaard surface in M. Then either the Hempel distance d(P) ≤ 2genus(Q) or P is isotopic to Q. This theorem can be naturally extended to bicompressible but weakly incompressible surfaces.

DOI : 10.2140/agt.2007.7.1119
Keywords: Heegaard splitting, incompressible surface, curve complex, sample layout

Li, Tao  1

1 Department of Mathematics, Boston College, Chestnut Hill, MA 02467, USA 
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Li, Tao. Saddle tangencies and the distance of Heegaard splittings. Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 1119-1134. doi: 10.2140/agt.2007.7.1119

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