Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Sphere stratifications and the Gauss map

M. C. Romero Fustera1*

a1 Department of Mathematics, University of Southampton, Southampton SO9 5NH


There is a residual subset of embeddings of an m-manifold, M in Rm+1 (m ≦ 6), for which the induced Maxwell subset on the sphere Sm is a stratified subset. We define and study two different stratifications of this subset and their extensions to the whole Sm: the Gauss stratification and the core stratification. We also find relations between the Euler numbers of the strata of the core stratification and the “exposed” singularities of the Gauss map on M.

(Received July 20 1982)

(Revised January 12 1983)


* This research was supported by a grant from M.E.C. (Spain).