A characterization of submanifolds by a homogeneity condition
Geometric Topology
2007-06-13 v2 Differential Geometry
Abstract
A very short proof of the following smooth homogeneity theorem of D. Repovs, E. V. Scepin and the author is presented. Let N be a locally compact subset of a smooth manifold M. Assume that for each two points x,y in N there exist their neighborhoods Ux and Uy in M and a diffeomorphism h : Ux \to Uy such that h(x)=y and h (Ux \cap N) = Uy \cap N. Then N is a smooth submanifold of M.
Cite
@article{arxiv.math/0606470,
title = {A characterization of submanifolds by a homogeneity condition},
author = {A. Skopenkov},
journal= {arXiv preprint arXiv:math/0606470},
year = {2007}
}
Comments
4 pages, meaning-distorting typos corrected