A structure theorem for irreducible open graph 3-manifolds
Geometric Topology
2025-04-09 v1
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.
Cite
@article{arxiv.2504.05769,
title = {A structure theorem for irreducible open graph 3-manifolds},
author = {Sylvain Maillot},
journal= {arXiv preprint arXiv:2504.05769},
year = {2025}
}