Volume 10, issue 3 (2010)

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Fibered orbifolds and crystallographic groups

John G Ratcliffe and Steven T Tschantz

Algebraic & Geometric Topology 10 (2010) 1627–1664
Abstract

In this paper, we prove that a normal subgroup N of an n–dimensional crystallographic group Γ determines a geometric fibered orbifold structure on the flat orbifold EnΓ, and conversely every geometric fibered orbifold structure on EnΓ is determined by a normal subgroup N of Γ. In particular, we prove that EnΓ is a fiber bundle, with totally geodesic fibers, over a β1–dimensional torus, where β1 is the first Betti number of Γ.

Keywords
fibered orbifold, flat orbifold, crystallographic group, space group
Mathematical Subject Classification 2000
Primary: 20H15
Secondary: 55R65, 57M50, 57S30
References
Publication
Received: 7 January 2010
Revised: 3 May 2010
Accepted: 1 June 2010
Published: 21 July 2010
Authors
John G Ratcliffe
Department of Mathematics
Vanderbilt University
Nashville TN 37240
Steven T Tschantz
Department of Mathematics
Vanderbilt University
Nashville TN 37240