### 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 t with respect to some point oe in its complement. The extensions of/to an orientation preserving immersion of the disc are classified up to topological equivalence by the (0, i(l — i-))-assemblages induced by a star of rays from oo to the complementary components of the curve. Applications to the classification problem of stable maps between closed surfaces are also discussed.

Original language | English (US) |
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Pages (from-to) | 87-93 |

Number of pages | 7 |

Journal | Proceedings of the American Mathematical Society |

Volume | 41 |

Issue number | 1 |

DOIs | |

State | Published - Nov 1973 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*41*(1), 87-93. https://doi.org/10.1090/S0002-9939-1973-0321112-0

**Spherical curves that bound immersed discs.** / Francis, George K.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 41, no. 1, pp. 87-93. https://doi.org/10.1090/S0002-9939-1973-0321112-0

}

TY - JOUR

T1 - Spherical curves that bound immersed discs

AU - Francis, George K.

PY - 1973/11

Y1 - 1973/11

N2 - Let/be an immersion of the oriented circle in the oriented sphere. Let the image lie in general position and have tangent winding number t with respect to some point oe in its complement. The extensions of/to an orientation preserving immersion of the disc are classified up to topological equivalence by the (0, i(l — i-))-assemblages induced by a star of rays from oo to the complementary components of the curve. Applications to the classification problem of stable maps between closed surfaces are also discussed.

AB - Let/be an immersion of the oriented circle in the oriented sphere. Let the image lie in general position and have tangent winding number t with respect to some point oe in its complement. The extensions of/to an orientation preserving immersion of the disc are classified up to topological equivalence by the (0, i(l — i-))-assemblages induced by a star of rays from oo to the complementary components of the curve. Applications to the classification problem of stable maps between closed surfaces are also discussed.

UR - http://www.scopus.com/inward/record.url?scp=84968469569&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84968469569&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1973-0321112-0

DO - 10.1090/S0002-9939-1973-0321112-0

M3 - Article

AN - SCOPUS:84968469569

VL - 41

SP - 87

EP - 93

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -