Singular limit laminations, Morse index, and positive scalar curvature

For any 3-manifold M 3 and any nonnegative integer g, we give here examples of metrics on M each of which has a sequence of embedded minimal surfaces of genus g and without Morse indexbounds. On any spherical space form we construct such a metric with positive scalar curvature. More generally, we construct such a metric with Scal ? 0 (and such surfaces) on any 3-manifold which carries a metric with Scal ? 0. ? 2004 Elsevier Ltd. All rights reserved.