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
- DOI: 10.1112/jlms/jdn089
- Enlaces
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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.
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