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.

Keywords

locally symmetric space, exotic smooth structure, duality, tangential map

Mathematical Subject Classification 2000

Primary: 53C35

Secondary: 57T15, 55R37, 57R99

References

Forward citations

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

Volume 2, issue 1 (2002)

Boris Okun