A note on the uniqueness of unstabilized Heegaard splittings of amalgamated 3-manifolds

Du, Kun; Qiu, Ruifeng

doi:10.1016/j.topol.2016.03.006

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Cited by 6 publications

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“…We will generalize this result to link and graph complements, with the additional benefit of avoiding many of the technical details of [7] necessary to treat the boundary components. Unfortunately, our bound will be worse than that obtained by Bachman and Schleimer, though it will be sufficient for many applications of this type of bound (e.g., [20], [15], [22], [5], and [21]). We note also that our proof requires a minimal starting position similar to that used by Hartshorn, an assumption the Bachman-Schleimer method was able to avoid.…”

Section: Definitionsmentioning

confidence: 69%

Hyperbolic manifolds containing high topological index surfaces

Campisi

Rathbun

2018

Pacific J. Math.

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If a graph is in bridge position in a 3-manifold so that the graph complement is irreducible and boundary irreducible, we generalize a result of Bachman and Schleimer to prove that the complexity of a surface properly embedded in the complement of the graph bounds the graph distance of the bridge surface. We use this result to construct, for any natural number n, a hyperbolic manifold containing a surface of topological index n.

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