Exotic smooth structures on nonpositively curved symmetric spaces

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.

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

References in corpus (1)

• Nonzero degree tangential maps between dual symmetric spaces

Cited by in corpus (3)

• Aspherical manifolds, relative hyperbolicity, simplicial volume and assembly maps
• Inertia Groups and Smooth Structures on Quaternionic Projective Spaces
• On submanifolds in locally symmetric spaces of noncompact type