Non-positively curved graph manifolds are virtually fibered over the circle

2001/08/02 by Svetlov, P.
#57M50 (Primary) 57M10 #57N10 #57N35 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.math/0108010

Abstract

In this note we prove that any closed graph manifold admitting a metric of non-positive sectional curvature (NPC-metric) has a finite cover, which is fibered over the circle. An explicit criterion to have a finite cover, which is fibered over the circle, is presented for the graph manifolds of certain class.

Related

• Homological properties of graph manifolds
• Obstructions for generalized graphmanifolds to be nonpositively curved
• Manifolds with conullity at most two as graph manifolds
• Topological and geometric properties of graph-manifolds
• Four-dimensional graph-manifolds with fundamental groups quasi-isometric to fundamental groups of orthogonal graph-manifolds