Homological properties of graph manifolds

Abstract

We consider the following properties of compact oriented irreducible graph-manifolds: to contain a ${\pi }_1$-injective surface (immersed, virtually embedded or embedded), be (virtually) fibered over $S^1$, 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.

17 pages