Geodesic
Exotic smooth structures on nonpositively curved symmetric spaces
Okun, Boris1
1Department of Mathematical Sciences, University of Wisconsin–Milwaukee, Milwaukee, WI 53201, USA
Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 381-389
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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.

DOI : 10.2140/agt.2002.2.381
Keywords: locally symmetric space, exotic smooth structure, duality, tangential map

Okun, Boris  1

1 Department of Mathematical Sciences, University of Wisconsin–Milwaukee, Milwaukee, WI 53201, USA 
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Okun, Boris. Exotic smooth structures on nonpositively curved symmetric spaces. Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 381-389. doi: 10.2140/agt.2002.2.381

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