$\pi_1$-injective surfaces in graph manifolds

Abstract.

A criterion is given for an immersed horizontal $\pi_1$-injective surface in a graph manifold to be separable. Examples are constructed of such surfaces, which are not separable and do not satisfy the k-plane property, for any k. It is shown that the simple loop conjecture holds in graph manifolds and that any graph manifold with boundary has an immersed horizontal surface.