Strong Haken via Sphere Complexes
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866910578887360512 |
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| author | Hensel, Sebastian Schultens, Jennifer |
| author_facet | Hensel, Sebastian Schultens, Jennifer |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_09831 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Strong Haken via Sphere Complexes Hensel, Sebastian Schultens, Jennifer Geometric Topology 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. |
| title | Strong Haken via Sphere Complexes |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2102.09831 |