Fundamental classes not representable by products

Details Fundamental classes not representable by products Fundamental classes not representable by products

2008-06-27

arxiv.org/abs/0806.4540v2

J. London Math. Soc. 79 (2009), 545--561

Mathematics

Geometric Topology

22 pages; updated references and corrected a typo; to appear in the Journal of the London Mathematical Society

Scientific paper

10.1112/jlms/jdn089

We prove that rationally essential manifolds with suitably large fundamental groups do not admit any maps of non-zero degree from products of closed manifolds of positive dimension. Particular examples include all manifolds of non-positive sectional curvature of rank one and all irreducible locally symmetric spaces of non-compact type. For closed manifolds from certain classes, say non-positively curved ones, or certain surface bundles 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.

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