Classifying immersed curves
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- by J. Scott Carter PDF
- Proc. Amer. Math. Soc. 111 (1991), 281-287 Request permission
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.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 111 (1991), 281-287
- MSC: Primary 57M05; Secondary 57M20, 57N05
- DOI: https://doi.org/10.1090/S0002-9939-1991-1043406-7
- MathSciNet review: 1043406