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

TL;DR

This paper proves that all closed graph manifolds with non-positive curvature have a finite cover that fibers over the circle, providing explicit criteria for certain classes of these manifolds.

Contribution

It establishes that non-positively curved graph manifolds are virtually fibered over the circle and offers explicit criteria for specific classes.

Findings

All closed NPC graph manifolds are virtually fibered.

Explicit criteria for fibered finite covers in certain classes.

Advances understanding of the structure of non-positively curved graph manifolds.

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.