On submanifolds in locally symmetric spaces of noncompact type
Abstract
Given a connected, compact, totally geodesic submanifold Ym of noncompact type inside a compact locally symmetric space of noncompact type Xn, we provide a sufficient condition that ensures that [Ym] is nonzero in Hm(Xn; R); in low dimensions, our condition is also necessary. We provide conditions under which there exist a tangential map of pairs from a finite cover (X-bar,Y-bar) to the nonnegatively curved duals (Xu,Yu).
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