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Sphere stratifications and the Gauss map

Published online by Cambridge University Press:  14 November 2011

M. C. Romero Fuster
M. C. Romero Fuster
Affiliation:
Department of Mathematics, University of Southampton, Southampton SO9 5NH
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Synopsis

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 95 , Issue 1-2 , 1983 , pp. 115 - 136
Copyright
Copyright © Royal Society of Edinburgh 1983

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