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On submanifolds in locally symmetric spaces of noncompact type

Jean-François Lafont and Benjamin Schmidt

Algebraic & Geometric Topology 6 (2006) 2455–2472

DOI: 10.2140/agt.2006.6.2455

arXiv: math.GT/0607242

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).

Keywords

locally symmetric space, duality, tangential map, Matsushima's map

Mathematical Subject Classification

Primary: 53C35

Secondary: 55R37, 57R42, 57R45, 57T15

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Publication

Received: 10 July 2006
Accepted: 9 November 2006
Published: 15 December 2006

Authors
Jean-François Lafont
Department of Mathematics
The Ohio State University
231 West 18th Avenue
Columbus, OH 43210-1174
Benjamin Schmidt
Department of Mathematics
University of Chicago
5734 S University Avenue
Chicago, IL 60637