An almost flat manifold with a cyclic or quaternionic holonomy group bounds
Differential Geometry
2016-05-18 v2 Algebraic Topology
Geometric Topology
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.
Keywords
Cite
@article{arxiv.1501.00300,
title = {An almost flat manifold with a cyclic or quaternionic holonomy group bounds},
author = {James F. Davis and Fuquan Fang},
journal= {arXiv preprint arXiv:1501.00300},
year = {2016}
}
Comments
8 pages, to appear in the Journal of Differential Geometry. New version of Lemma 2.5: A manifold bounds if there is an involution on TM whose fixed bundle is full rank