Key points are not available for this paper at this time.
Background 1. Statement of main results and outline of their proof II.Preliminaries 2. Smoothing Hausdorff approximations 3. Equivariant and parameterized version of the theorem on almost flat manifolds 4. Nilpotent Killing structures on fibrations III.The nilpotent Killing structure and invariant round metric 5. Local fibration of the frame bundle 6. Making the local fibrations compatible 7. Making the local group actions compatible 8.The induced structure and metric on the base Appendix 1. Local structure of Riemannian manifolds of bounded curvature
Cheeger et al. (Wed,) studied this question.