The strong Haken theorem via sphere complexes
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 S 1 summand, any Heegaard splitting of M restricts to the standard Heegaard splitting on the summand.
Authors
- Sebastian Hensel (ORCID: https://orcid.org/0000-0002-9369-4173)
- Jennifer Schultens (ORCID: https://orcid.org/0000-0003-3898-0051)
Institutions
- LMU Klinikum (DE)
- Ludwig-Maximilians-Universität München (DE)
- University of California, Davis (US)
Publication Details
- Journal
- Algebraic & Geometric Topology
- Published
- 2024-08-19
- DOI
- https://doi.org/10.2140/agt.2024.24.2707
- Citations
- 2
- Primary Topic
- Geometric and Algebraic Topology
- Type
- article
- Field-Weighted Citation Impact
- 2.02