Spherical curves that bound immersed discs

George K Francis

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)87-93
Number of pages7
JournalProceedings of the American Mathematical Society
Volume41
Issue number1
DOIs
StatePublished - Nov 1973

Fingerprint

Immersion
Stars
Topological Equivalence
Stable Map
Winding number
Curve
Classification Problems
Tangent line
Half line
Star
Circle
Complement
Closed

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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

In: Proceedings of the American Mathematical Society, Vol. 41, No. 1, 11.1973, p. 87-93.

Research output: Contribution to journalArticle

Francis, George K. / Spherical curves that bound immersed discs. In: Proceedings of the American Mathematical Society. 1973 ; Vol. 41, No. 1. pp. 87-93.
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