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

Classifying immersed curves


Author: J. Scott Carter
Journal: Proc. Amer. Math. Soc. 111 (1991), 281-287
MSC: Primary 57M05; Secondary 57M20, 57N05
MathSciNet review: 1043406
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Abstract: Let a collection $ \gamma $ of generically immersed curves be given in an oriented surface $ G$. To each component circle, associate a Gauss word by traveling once around the circle and recording the crossing points with signs. The set of these words forms a Gauss paragraph. If $ {\gamma _1}$ and $ {\gamma _2}$ fill the surface $ G$ in the sense that the complementary regions are disks, then there is a homeomorphism of $ G$ taking one to the other if and only if $ {\gamma _1}$ and $ {\gamma _2}$ have isomorphic Gauss paragraphs. This notion of isomorphism is defined here; it ignores the choices made in defining the Gauss words.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1043406-7
PII: S 0002-9939(1991)1043406-7
Article copyright: © Copyright 1991 American Mathematical Society