On submanifolds in locally symmetric spaces of noncompact type

Details On submanifolds in locally symmetric spaces of noncompact type On submanifolds in locally symmetric spaces of noncompact type

2006-07-10

arxiv.org/abs/math/0607242v2

Algebr. Geom. Topol. 6 (2006) 2455-2472

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 15 December 2006

Scientific paper

10.2140/agt.2006.6.2455

Given a connected, compact, totally geodesic submanifold Y^m of noncompact type inside a compact locally symmetric space of noncompact type X^n, we provide a sufficient condition that ensures that [Y^m] is nonzero in H_m(X^n; 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 (X_u,Y_u).

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