On submanifolds in locally symmetric spaces of noncompact type
Copyright policy )On submanifolds in locally symmetric spaces of noncompact type
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).
This is the version published by Algebraic & Geometric Topology on 15 December 2006
- THE OHIO STATE UNIVERSITY United States
- University of Chicago United States
- The Ohio State University United States
Matsushima's map, Mathematics - Differential Geometry, Maps between classifying spaces in algebraic topology, locally symmetric space, tangential map, Immersions in differential topology, Global submanifolds, Geometric Topology (math.GT), 53C35, Mathematics - Geometric Topology, Differential Geometry (math.DG), Homology and cohomology of homogeneous spaces of Lie groups, 57R42, FOS: Mathematics, duality, 57R45, 53C35, 55R37, 57R42, 57R45, 57T15, 57T15, Differential geometry of symmetric spaces, Singularities of differentiable mappings in differential topology, 55R37
Matsushima's map, Mathematics - Differential Geometry, Maps between classifying spaces in algebraic topology, locally symmetric space, tangential map, Immersions in differential topology, Global submanifolds, Geometric Topology (math.GT), 53C35, Mathematics - Geometric Topology, Differential Geometry (math.DG), Homology and cohomology of homogeneous spaces of Lie groups, 57R42, FOS: Mathematics, duality, 57R45, 53C35, 55R37, 57R42, 57R45, 57T15, 57T15, Differential geometry of symmetric spaces, Singularities of differentiable mappings in differential topology, 55R37
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