Fundamental classes not representable by products

• Autores: D. Kotschick, C. Löh
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 79, Nº 3, 2009, págs. 545-561
• Idioma: inglés
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• Resumen

  • 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.