Heegaard splittings of Haken manifolds have bounded distance

By K. Hartshorn. 2002

86 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/80682900ee398463aaeced8eddd1e31bb89f445d

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The amalgamation of high distance Heegaard splittings is always efficient (2008, background): “Lemma 3.2 ([ 4 ,10]) Let M = V ∪S W be a Heegaard splitting, and F be an incompressible surface in M. Then either F can be isotoped to be disjoint from S or d(S) ≤ 2 − χ( F).”
Multiple bridge surfaces restrict knot distance (2005, background): “For example in [4] Hartshorn shows that the Euler characteristic of an essential surface in a manifold bounds the distance of any of its Heegaard splittings.”
Heegaard Splittings and Pseudo-Anosov Maps (2009, result): “Compare the above result with the of K. Hartshorn [ Ha02 ] where by using purely topological methods he is able to bound from below the genus of an embedded 1-injective surface in terms of the splitting.”
Heegaard surfaces and the distance of amalgamation (2008, background): “By Hartshorn’s theorem [5] (another proof is in [15]), either Fi \F D∅ after isotopy or d.”
Alternate Heegaard genus bounds distance (2005, result): “In the former case, the result follows from Hartshorn’s theorem [4] (see also [9]).”
Random walks on the mapping class group (2006, background): “ one. If a manifold has Heegaard splitting distance greater than two then this implies that the manifold is hyperbolic, by Kobayashi [15] or Hempel [9], assuming geometrization. In fact, by Hartshorn [8], this shows that the probability that M(wn) contains an incompressible surface of genus at most ”
The geometry of the disk complex (2010, background): “5 does not hold in general; this is a fundamental observation due to Kobayashi [27] (see also [21]).”