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Exotic smooth structures on nonpositively curved symmetric spaces

Boris Okun

Algebraic & Geometric Topology 2 (2002) 381–389

arXiv: math.DG/0206291

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
Mathematical Subject Classification 2000
Primary: 53C35
Secondary: 57T15, 55R37, 57R99
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Publication
Received: 14 January 2002
Revised: 16 May 2002
Accepted: 17 May 2002
Published: 22 May 2002
Authors
Boris Okun
Department of Mathematical Sciences
University of Wisconsin–Milwaukee
Milwaukee, WI 53201
USA