Journal of Differential Geometry

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

James F. Davis and Fuquan Fang

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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.

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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.

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