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Sphere stratifications and the Gauss map

  • M. C. Romero Fuster (a1)
Synopsis
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.

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1Arnold V. I.. Critical points of smooth functions and their normal forms. Russian Math. Surveys 30:5 (1975), 175.
2Banchoff T., Gaffney T. and McCrory C.. Cusps of Gauss Mappings. Research Notes in Mathematics (London: Pitman, 1982).
3Bruce J. W.. Duals of generic hypersurfaces. Math. Scand. 49 (1981), 3660.
4Gibson C. G., Wirthmuller K., du Plessis A. A. and Looijenga E. N. J.. Topological stability of smooth mappings. Lecture Notes in Mathematics 552 (Berlin: Springer, 1976).
5Looijenga E. N. J.. Structural stability of smooth families of C∞-functions (Doctoral thesis, Univ. of Amsterdam, 1974).
6Mather J.. Stratifications and mappings. In Dynamical Systems, ed. Peixoto M. M. (New York: Academic Press, 1973).
7Robertson S. A.. The dual of a height function. J. London Math. Soc. 8 (1974), 187192.
8Robertson S. A. and Romero Fuster M. C.. Convex hulls of hypersurfaces, to appear.
9Romero Fuster M. C.. The convex hull of an immersion (Ph.D. thesis, Southampton Univ., 1981).
10Thorn R.. Sur le cut-locus d'une variete plongée. J. Differential Geom. 6 (1972), 577586.
11Thorn R.. Stabilité structurelle et morphogénèse (Reading, Mass.: Benjamin, 1972).
12Trotman D. J. A. and Zeeman E. C.. The classification of elementary catastophes of codimension ≦5. In Structural Stability, the Theory of Catastophes and Applications in the Sciences, Seattle 1975.Lecture Notes in Mathematics 525 (Berlin: Springer, 1976).
13Wall C. T. C.. Geometric properties of generic differentiable manifolds. In Geometry and Topology, Rio de Janeiro 1976. Lecture Notes in Mathematics 597, 707774 (Berlin: Springer, 1977).
14Wasserman G.. 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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