Spherical curves that bound immersed discs

Author:
George K. Francis

Journal:
Proc. Amer. Math. Soc. **41** (1973), 87-93

MSC:
Primary 57D40

DOI:
https://doi.org/10.1090/S0002-9939-1973-0321112-0

MathSciNet review:
0321112

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Abstract: Let be an immersion of the oriented circle in the oriented sphere. Let the image lie in general position and have tangent winding number with respect to some point in its complement. The extensions of to an orientation preserving immersion of the disc are classified up to topological equivalence by the -assemblages induced by a star of rays from to the complementary components of the curve. Applications to the classification problem of stable maps between closed surfaces are also discussed.

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DOI:
https://doi.org/10.1090/S0002-9939-1973-0321112-0

Article copyright:
© Copyright 1973
American Mathematical Society