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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

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