Nonzero degree tangential maps between dual symmetric spaces

Abstract

We construct a tangential map from a locally symmetric space of noncompact type to its dual compact type twin. By comparing the induced map in cohomology to a map defined by Matsushima, we conclude that in the equal rank case the map has a nonzero degree.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-35.abs.html

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• On negatively curved bundles with hyperbolic fibers outside the Igusa stable range