Geodesic
Fibered orbifolds and crystallographic groups
Ratcliffe, John G1 ; Tschantz, Steven T1
1Department of Mathematics, Vanderbilt University, Nashville TN 37240
Algebraic and Geometric Topology, Tome 10 (2010) no. 3, pp. 1627-1664
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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 En∕Γ, and conversely every geometric fibered orbifold structure on En∕Γ is determined by a normal subgroup N of Γ. In particular, we prove that En∕Γ is a fiber bundle, with totally geodesic fibers, over a β1–dimensional torus, where β1 is the first Betti number of Γ.

DOI : 10.2140/agt.2010.10.1627
Keywords: fibered orbifold, flat orbifold, crystallographic group, space group

Ratcliffe, John G  1   ; Tschantz, Steven T  1

1 Department of Mathematics, Vanderbilt University, Nashville TN 37240 
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Ratcliffe, John G; Tschantz, Steven T. Fibered orbifolds and crystallographic groups. Algebraic and Geometric Topology, Tome 10 (2010) no. 3, pp. 1627-1664. doi: 10.2140/agt.2010.10.1627

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