On submanifolds in locally symmetric spaces of noncompact type

Lafont, Jean-François; Schmidt, Benjamin

doi:10.2140/agt.2006.6.2455

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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 $Y^{m}$ of noncompact type inside a compact locally symmetric space of noncompact type $X^{n}$ , we provide a sufficient condition that ensures that $[Y^{m}] \neq 0 \in H_{m} (X^{n}; ℝ)$ ; in low dimensions, our condition is also necessary. We provide conditions under which there exist a tangential map of pairs from a finite cover $(\bar{X}, \bar{Y})$ to the nonnegatively curved duals $(X_{u}, Y_{u})$ .

Keywords

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

Mathematical Subject Classification 2000

Primary: 53C35

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

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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

Volume 6, issue 5 (2006)