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The strong Haken theorem via sphere complexes

Sebastian Hensel and Jennifer Schultens

Algebraic & Geometric Topology 24 (2024) 2707–2719
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 S2 × S1 summand, any Heegaard splitting of M restricts to the standard Heegaard splitting on the summand.

Keywords
Heegaard splitting, Haken sphere, strong Haken theorem
Mathematical Subject Classification
Primary: 57K30
References
Publication
Received: 6 July 2022
Revised: 6 February 2023
Accepted: 20 June 2023
Published: 19 August 2024
Authors
Sebastian Hensel
Department Mathematisches Institut
LMU München
Munich
Germany
Jennifer Schultens
Department of Mathematics
University of California Davis
Davis, CA
United States

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