Generic Immersions of the Two-Sphere to R3 and Their Skeletons

Author： Stepanova M.  

Publisher： Springer Publishing Company

ISSN： 1072-3374

Source： Journal of Mathematical Sciences, Vol.131, Iss.1, 2005-11, pp. : 5428-5437

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Abstract

Let f:S 2 ↬ R 3 be a generic smooth immersion. The skeleton of f is the following triple (Γ, D, p): Γ ⊂ R 3 is the 1-polyhedron of singular points of f, D = f−1(Γ) ⊂ S 2 is also a 1-polyhedron, and p : D → Γ, x ↦ f(x), is the projection. For triples of the form (D,Γ,p), where Γ has at most four vertices, we give an iff-condition under which the triple is the skeleton of a smooth immersion f : S 2 ↬ R 3. Bibliography: 4 titles.

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