Exotic smooth structures on nonpositively curved symmetric spaces

Details Exotic smooth structures on nonpositively curved symmetric spaces Exotic smooth structures on nonpositively curved symmetric spaces

2002-06-27

arxiv.org/abs/math/0206291v1

Algebr. Geom. Topol. 2 (2002) 381-389

Mathematics

Differential Geometry

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-18.abs.html

Scientific paper

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 its dual compact type twin.

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