AN ALMOST FLAT MANIFOLD WITH A CYCLIC OR QUATERNIONIC HOLONOMY GROUP BOUNDS

作者:Davis, James F.*; Fang, Fuquan*
来源:Journal of Differential Geometry, 2016, 103(2): 289-296.
DOI:10.4310/jdg/1463404119

摘要

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.