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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57M05, 57M20, 57N05

Retrieve articles in all journals with MSC: 57M05, 57M20, 57N05

Additional Information

Article copyright: © Copyright 1991 American Mathematical Society