A structure theorem for irreducible open graph 3-manifolds
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916678626967552 |
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| author | Maillot, Sylvain |
| author_facet | Maillot, Sylvain |
| contents | Graph manifolds are a class of compact, orientable 3-manifolds introduced in 1967 by Waldhausen as a generalization of Seifert fibered 3-manifolds. From the point of view of Thurston's geometrization program, graph manifolds are exactly the compact, orientable 3-manifolds without any hyperbolic piece in their geometric decomposition. In this article we consider a generalization of the notion of graph manifold that includes some noncompact 3-manifolds. We prove a structure theorem for irreducible open graph manifolds in the form of a canonical 'reduced' decomposition along embedded, incompressible 2-tori. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05769 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A structure theorem for irreducible open graph 3-manifolds Maillot, Sylvain Geometric Topology Graph manifolds are a class of compact, orientable 3-manifolds introduced in 1967 by Waldhausen as a generalization of Seifert fibered 3-manifolds. From the point of view of Thurston's geometrization program, graph manifolds are exactly the compact, orientable 3-manifolds without any hyperbolic piece in their geometric decomposition. In this article we consider a generalization of the notion of graph manifold that includes some noncompact 3-manifolds. We prove a structure theorem for irreducible open graph manifolds in the form of a canonical 'reduced' decomposition along embedded, incompressible 2-tori. |
| title | A structure theorem for irreducible open graph 3-manifolds |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2504.05769 |