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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Abstract

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.

Article information

Source
J. Differential Geom., Volume 103, Number 2 (2016), 289-296.

Dates
First available in Project Euclid: 16 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1463404119

Digital Object Identifier
doi:10.4310/jdg/1463404119

Mathematical Reviews number (MathSciNet)
MR3504950

Zentralblatt MATH identifier
1350.53064

Citation

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


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