Algebraic & Geometric Topology Volume 2, issue 1 (2002)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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All flat manifolds are cusps of hyperbolic orbifolds

Darren D Long and Alan W Reid

Algebraic & Geometric Topology 2 (2002) 285–296

DOI: 10.2140/agt.2002.2.285

arXiv: math.GT/0204238

Abstract

We show that all closed flat $n$ –manifolds are diffeomorphic to a cusp cross-section in a finite volume hyperbolic $(n + 1)$ –orbifold.

Keywords

flat manifolds, hyperbolic orbifold, cusp cross-sections

Mathematical Subject Classification 2000

Primary: 57M50

Secondary: 57R99

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Publication

Received: 6 December 2001

Accepted: 10 April 2002

Published: 18 April 2002

Authors

Darren D Long
Department of Mathematics University of California Santa Barbara, CA 93106 USA

Alan W Reid
Department of Mathematics University of Texas Austin, TX 78712 USA