An almost flat manifold with a cyclic or quaternionic holonomy group bounds

摘要

A long-standing conjecture of Farrell and Zdravkovska and independentlyS.~T.~Yau states that every almost flat manifold is the boundary of a compactmanifold. This paper gives a simple proof of this conjecture when the holonomygroup is cyclic or quaternionic. The proof is based on the interaction betweenflat bundles and involutions.