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2010 Fibered orbifolds and crystallographic groups
John G Ratcliffe, Steven T Tschantz
Algebr. Geom. Topol. 10(3): 1627-1664 (2010). DOI: 10.2140/agt.2010.10.1627

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.

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John G Ratcliffe. Steven T Tschantz. "Fibered orbifolds and crystallographic groups." Algebr. Geom. Topol. 10 (3) 1627 - 1664, 2010. https://doi.org/10.2140/agt.2010.10.1627

Information

Received: 7 January 2010; Revised: 3 May 2010; Accepted: 1 June 2010; Published: 2010
First available in Project Euclid: 19 December 2017

zbMATH: 1245.57026
MathSciNet: MR2683747
Digital Object Identifier: 10.2140/agt.2010.10.1627

Subjects:
Primary: 20H15
Secondary: 55R65, 57M50, 57S30

Rights: Copyright © 2010 Mathematical Sciences Publishers

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