Spherical curves that bound immersed discs

Francis, George K.

doi:10.1090/S0002-9939-1973-0321112-0

Spherical curves that bound immersed discs
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by George K. Francis

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

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

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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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