Journal of Differential Geometry
- J. Differential Geom.
- Volume 103, Number 2 (2016), 289-296.
An almost flat manifold with a cyclic or quaternionic holonomy group bounds
A long-standing conjecture of Farrell and Zdravkovska and independently S.T. Yau states that every almost flat manifold is the boundary of a compact manifold. This paper gives a simple proof of this conjecture when the holonomy group is cyclic or quaternionic. The proof is based on the interaction between flat bundles and involutions.
J. Differential Geom., Volume 103, Number 2 (2016), 289-296.
First available in Project Euclid: 16 May 2016
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Davis, James F.; Fang, Fuquan. An almost flat manifold with a cyclic or quaternionic holonomy group bounds. J. Differential Geom. 103 (2016), no. 2, 289--296. doi:10.4310/jdg/1463404119. https://projecteuclid.org/euclid.jdg/1463404119