Homological properties of graph manifolds

2001/12/31 by P. Svetlov, Svetlov, P.
Computer Science · Mathematics · #57M50 (Primary) 57M10 #57N10 #57N35 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.GT #msc:57M10 #msc:57M50 #msc:57N10 #msc:57N35

paper · pdf · doi:10.48550/arxiv.math/0112308

17 pages

openalex publication_date 2001/12/31 · arxiv created 2002/01/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the following properties of compact oriented irreducible graph-manifolds: to contain a π₁-injective surface (immersed, virtually embedded or embedded), be (virtually) fibered over S¹, and to carry a metric of nonpositive sectional curvature. It turns out that all these properties can be described from a unified point of view.

Citations

• Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle

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• Non-positively curved graph manifolds are virtually fibered over the circle
• A structure theorem for irreducible open graph 3-manifolds
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