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Sphere stratifications and the Gauss map

  • M. C. Romero Fuster (a1)

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.

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4 C. G. Gibson , K. Wirthmuller , A. A. du Plessis and E. N. J. Looijenga . Topological stability of smooth mappings. Lecture Notes in Mathematics 552 (Berlin: Springer, 1976).

13 C. T. C. Wall . Geometric properties of generic differentiable manifolds. In Geometry and Topology, Rio de Janeiro 1976. Lecture Notes in Mathematics 597, 707774 (Berlin: Springer, 1977).

14 G. Wasserman . Stability of unfoldings. Lecture Notes in Mathematics 393 (Berlin: Springer, 1974).

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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