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Strong Haken via Sphere Complexes

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arxiv 2102.09831 v1 pith:6ARN44YQ submitted 2021-02-19 math.GT

Sebastian Hensel , Jennifer Schultens This is my paper · ORCID
classification math.GT
keywords hakenheegaardmanifoldsspheresplittingstrongsummandapplication
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abstract

We give a short proof of Scharlemann's Strong Haken Theorem for closed $3$-manifolds (and manifolds with spherical boundary). As an application, we also show that given a decomposing sphere $R$ for a $3$-manifold $M$ that splits off an $S^2 \times S^1$ summand, any Heegaard splitting of $M$ restricts to the standard Heegaard splitting on the summand.

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  1. Genus three Goeritz groups of connected sums of two lens spaces

    math.GT 2024-11 conditional novelty 6.0 of 10

    For any genus-three reducible Heegaard splitting of a connected sum of two lens spaces, the Goeritz group is finitely generated and the reducing sphere complex is connected.

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