Algebraic and Geometric Topology 2 (2002),
paper no. 18, pages 381-389.
Exotic smooth structures on nonpositively curved symmetric spaces
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.
Locally symmetric space, exotic smooth structure, duality, tangential map
AMS subject classification.
Secondary: 57T15, 55R37, 57R99.
Submitted: 14 January 2002.
(Revised: 16 May 2002.)
Accepted: 17 May 2002.
Published: 22 May 2002.
Notes on file formats
Department of Mathematical Sciences, University of Wisconsin-Milwaukee
Milwaukee, WI 53201, USA
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