Algebraic and Geometric Topology 2 (2002), paper no. 18, pages 381-389.

Exotic smooth structures on nonpositively curved symmetric spaces

Boris Okun

Abstract. 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.

Keywords. Locally symmetric space, exotic smooth structure, duality, tangential map

AMS subject classification. Primary: 53C35. Secondary: 57T15, 55R37, 57R99.

DOI: 10.2140/agt.2002.2.381

E-print: arXiv:math.DG/0206291

Submitted: 14 January 2002. (Revised: 16 May 2002.) Accepted: 17 May 2002. Published: 22 May 2002.

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Boris Okun
Department of Mathematical Sciences, University of Wisconsin-Milwaukee
Milwaukee, WI 53201, USA
Email: okun@uwm.edu

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