Factorizations of generic mappings between surfaces

Luminati, Domenico

doi:10.1090/S0002-9939-1993-1170547-8

Factorizations of generic mappings between surfaces
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by Domenico Luminati PDF

Proc. Amer. Math. Soc. 118 (1993), 247-253 Request permission

Abstract:

Given a generic mapping $F:{\mathbf {S}} \to {\mathbf {N}}$ of two smooth (i.e., ${C^\infty }$) real surfaces, ${\mathbf {S}}$ compact, and a line bundle $\pi :{\mathbf {E}} \to {\mathbf {N}}$, we look for necessary and sufficient conditions to find an immersion $\tilde F:{\mathbf {S}} \to {\mathbf {E}}$ such that $F = \pi \circ \tilde F$.

References

Th. Bröcker, Differentiable germs and catastrophes, London Mathematical Society Lecture Note Series, No. 17, Cambridge University Press, Cambridge-New York-Melbourne, 1975. Translated from the German, last chapter and bibliography by L. Lander. MR 0494220
André Haefliger, Quelques remarques sur les applications différentiables d’une surface dans le plan, Ann. Inst. Fourier (Grenoble) 10 (1960), 47–60 (French). MR 116357
Kenneth C. Millett, Generic smooth maps of surfaces, Topology Appl. 18 (1984), no. 2-3, 197–215. MR 769291, DOI 10.1016/0166-8641(84)90010-5
Roberto Pignoni, On surfaces and their contours, Manuscripta Math. 72 (1991), no. 3, 223–249. MR 1118544, DOI 10.1007/BF02568277
Norman Steenrod, The Topology of Fibre Bundles, Princeton Mathematical Series, vol. 14, Princeton University Press, Princeton, N. J., 1951. MR 0039258
Hassler Whitney, On singularities of mappings of euclidean spaces. I. Mappings of the plane into the plane, Ann. of Math. (2) 62 (1955), 374–410. MR 73980, DOI 10.2307/1970070