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An exhaustion of locally symmetric spaces by compact submanifolds with corners

Identifieur interne : 001C83 ( Main/Exploration ); précédent : 001C82; suivant : 001C84

An exhaustion of locally symmetric spaces by compact submanifolds with corners

Auteurs : Enrico Leuzinger [Suisse]

Source :

RBID : ISTEX:33E2AF6547032913962C5A43884843D20BC7051E

English descriptors

Abstract

Abstract: LetX be a Riemannian symmetric space of noncompact type and rank≧2 and let Γ be a non-uniform, irreducible lattice. On the locally symmetric quotientV=Γ/X we construct an exhaustion functionh:V→[0,∞) whose sublevel sets {h≦s} are compact submanifolds ofV with corners. The top dimensional boundary faces of {h≦s} are parts of certain horospheres that join together at the corners. It can be shown that actually {h≦s} is a submanifold with corners isomorphic to the Borel-Serre compactification ofV.

Url:
DOI: 10.1007/BF01884305


Affiliations:


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<div type="abstract" xml:lang="en">Abstract: LetX be a Riemannian symmetric space of noncompact type and rank≧2 and let Γ be a non-uniform, irreducible lattice. On the locally symmetric quotientV=Γ/X we construct an exhaustion functionh:V→[0,∞) whose sublevel sets {h≦s} are compact submanifolds ofV with corners. The top dimensional boundary faces of {h≦s} are parts of certain horospheres that join together at the corners. It can be shown that actually {h≦s} is a submanifold with corners isomorphic to the Borel-Serre compactification ofV.</div>
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