A structure theorem for irreducible open graph 3-manifolds

2025/04/08 by Maillot, Sylvain
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2504.05769

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.

Related

• Locally Collapsed 3-Manifolds
• Characterizing families of graph manifolds via suitable classes of simple fold maps into the plane and embeddability of the Reeb spaces in some 3-dimensional manifolds
• Profinite rigidity of graph manifolds and JSJ decompositions of 3-manifolds
• Profinite properties of graph manifolds
• Homological properties of graph manifolds