5
$\begingroup$

In his talk Misha Gromov- How does he do it, Jeff Cheeger mentions a theorem of Gromov proved sometime in the early 70's. Theorem: Every manifold admitting a sequence of metrics such that the diameter and curvature go to zero is finitely covered by a nilmanifold. Further, he says that the proof is not easy even today; something usually associated with Gromov! It would be great to read the original paper, and even better if some book contains it. Please help me find them. Thanks.

$\endgroup$
1
  • 1
    $\begingroup$ I would like to add Ruh's extension to Gromov's paper "Almost flat manifolds" J. Differential Geom. 17 (1982), no. 1, 1–14. $\endgroup$
    – J. GE
    Feb 5, 2014 at 20:30

2 Answers 2

8
$\begingroup$

M. Gromov, Almost flat manifolds, J. Differential Geometry 13 (1978) 231-241

online at http://seven.ihes.fr/~gromov/PDF/3[20].pdf

$\endgroup$
7
$\begingroup$

The book "Gromov's almost flat manifolds" by Buser and Karcher is a nice exposition of Gromov's result.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.