Fundamental classes not representable by products
D. Kotschick, C. L Öh · 2013
Abstract. We prove that rationally essential manifolds with suitably large fundamental groups do not admit any maps of non-zero degree from prod-ucts of closed manifolds of positive dimension. Particular examples include all manifolds of non-positive sectional curvature of rank one and all irre-ducible locally symmetric spaces of non-compact type. For closed manifolds from certain classes, say non-positively curved ones, or certain surface bun-dles over surfaces, we show that they do admit maps of non-zero degree from non-trivial products if and only if they are virtually diffeomorphic to products. 1.