Geodesic
On submanifolds in locally symmetric spaces of noncompact type
Lafont, Jean-François1 ; Schmidt, Benjamin2
1Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210-1174
2Department of Mathematics, University of Chicago, 5734 S University Avenue, Chicago, IL 60637
Algebraic and Geometric Topology, Tome 6 (2006) no. 5, pp. 2455-2472
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Given a connected, compact, totally geodesic submanifold Y m of noncompact type inside a compact locally symmetric space of noncompact type Xn, we provide a sufficient condition that ensures that [Y m]≠0 ∈ 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 (X̄,Y ̄) to the nonnegatively curved duals (Xu,Y u).

DOI : 10.2140/agt.2006.6.2455
Keywords: locally symmetric space, duality, tangential map, Matsushima's map

Lafont, Jean-François  1   ; Schmidt, Benjamin  2

1 Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210-1174
2 Department of Mathematics, University of Chicago, 5734 S University Avenue, Chicago, IL 60637 
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Lafont, Jean-François; Schmidt, Benjamin. On submanifolds in locally symmetric spaces of noncompact type. Algebraic and Geometric Topology, Tome 6 (2006) no. 5, pp. 2455-2472. doi: 10.2140/agt.2006.6.2455

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