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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Spherical curves that bound immersed discs


Author: George K. Francis
Journal: Proc. Amer. Math. Soc. 41 (1973), 87-93
MSC: Primary 57D40
MathSciNet review: 0321112
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Abstract: Let $ f$ be an immersion of the oriented circle in the oriented sphere. Let the image lie in general position and have tangent winding number $ \tau $ with respect to some point $ \infty $ in its complement. The extensions of $ f$ to an orientation preserving immersion of the disc are classified up to topological equivalence by the $ (0,\tfrac{1}{2}(1 - \tau ))$-assemblages induced by a star of rays from $ \infty $ 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: http://dx.doi.org/10.1090/S0002-9939-1973-0321112-0
PII: S 0002-9939(1973)0321112-0
Article copyright: © Copyright 1973 American Mathematical Society