Algebraic and Geometric Topology 2 (2002), paper no. 13, pages 285-296.

All flat manifolds are cusps of hyperbolic orbifolds

D.D. Long, A.W. Reid

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

AMS subject classification. Primary: 57M50. Secondary: 57R99.

DOI: 10.2140/agt.2002.2.285

E-print: arXiv:math.GT/0204238

Submitted: 6 December 2001. Accepted: 10 April 2002. Published: 18 April 2002.

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D.D. Long, A.W. Reid
Department of Mathematics, University of California
Santa Barbara, CA 93106, USA
and
Department of Mathematics, University of Texas
Austin, TX 78712, USA

Email: long@math.ucsb.edu, areid@math.utexas.edu

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