A structure theorem for irreducible open graph 3-manifolds

Sylvain Maillot

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arXiv · 2504.05769

A structure theorem for irreducible open graph 3-manifolds

Sylvain Maillot

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Abstract

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.

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Sylvain Maillot. 2025-04-08. A structure theorem for irreducible open graph 3-manifolds. https://arxiv.org/abs/2504.05769

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