A characterization of submanifolds by a homogeneity condition

Details A characterization of submanifolds by a homogeneity condition A characterization of submanifolds by a homogeneity condition

2006-06-19

arxiv.org/abs/math/0606470v2

Topol. Appl. 154 (2007) 1894-1897

Mathematics

Geometric Topology

4 pages, meaning-distorting typos corrected

Scientific paper

10.1016/j.topol.2007.03.002

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.

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