All flat manifolds are cusps of hyperbolic orbifolds

Darren D Long, Alan W Reid
2002 Algebraic and Geometric Topology  
We show that all closed flat n-manifolds are diffeomorphic to a cusp cross-section in a finite volume hyperbolic (n+1)-orbifold.
doi:10.2140/agt.2002.2.285 fatcat:hgwm4hl5tnbp5afyfxubovqzsu