Saddle tangencies and the distance of Heegaard splittings

Li, Tao

doi:10.2140/agt.2007.7.1119

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Saddle tangencies and the distance of Heegaard splittings

Tao Li

Algebraic & Geometric Topology 7 (2007) 1119–1134

DOI: 10.2140/agt.2007.7.1119

arXiv: math.GT/0701396

Abstract

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 $d (P) \leq 2 genus (Q)$ or $P$ is isotopic to $Q$ . This theorem can be naturally extended to bicompressible but weakly incompressible surfaces.

Keywords

Heegaard splitting, incompressible surface, curve complex, sample layout

Mathematical Subject Classification 2000

Primary: 57N10

Secondary: 57M50

References

Publication

Received: 7 January 2007

Revised: 1 June 2007

Accepted: 25 July 2007

Published: 2 August 2007

Authors

Tao Li
Department of Mathematics Boston College Chestnut Hill, MA 02467 USA
http://www2.bc.edu/~taoli/

Volume 7, issue 2 (2007)