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Exotic smooth structures on nonpositively curved symmetric spaces. (English) Zbl 0998.53033
Summary: We construct series of examples of exotic smooth structures on compact locally symmetric spaces of noncompact type. In particular, we obtain higher rank examples, which do not support Riemannian metric of nonpositive curvature. The examples are obtained by taking the connected sum with an exotic sphere. To detect the change of the smooth structure we use a tangential map from the locally symmetric space to its dual of compact type.

MSC:
53C35 Differential geometry of symmetric spaces
57R55 Differentiable structures in differential topology
57R99 Differential topology
57T15 Homology and cohomology of homogeneous spaces of Lie groups
55R37 Maps between classifying spaces in algebraic topology
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