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Some non-symmetric manifolds. (English) Zbl 0795.53038
Szenthe, J. (ed.) et al., Differential geometry and its applications. Proceedings of a colloquium, held in Eger, Hungary, August 20-25, 1989, organized by the János Bolyai Mathematical Society. Amsterdam: North- Holland Publishing Company. Colloq. Math. Soc. János Bolyai. 56, 535-546 (1992).
A manifold \(M\) is called aspherical if its universal cover is contractible. Typical examples of aspherical manifolds are the connected complete locally symmetric Riemannian manifolds without compact de Rham factors. Examples of compact aspherical manifolds that are not diffeomorphic to any locally symmetric manifold are obtained. The author constructs five- and seven-dimensional compact aspherical smooth manifolds that are not homotopy equivalent to any compact locally symmetric manifold.
For the entire collection see [Zbl 0764.00002].

MSC:
53C20 Global Riemannian geometry, including pinching
53C35 Differential geometry of symmetric spaces
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