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

 

On self-intersections of immersed surfaces


Author: Gui-Song Li
Journal: Proc. Amer. Math. Soc. 126 (1998), 3721-3726
MSC (1991): Primary 57M42
MathSciNet review: 1459134
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Abstract: A daisy graph is a union of immersed circles in 3-space which intersect only at the triple points. It is shown that a daisy graph can always be realized as the self-intersection set of an immersed closed surface in 3-space and the surface may be chosen to be orientable if and only if the daisy graph has an even number of edges on each immersed circle.


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Additional Information

Gui-Song Li
Affiliation: Institute of Systems Science, Academia Sinica, Beijing 100080, People’s Republic of China
Email: lgs@iss06.iss.ac.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04456-6
PII: S 0002-9939(98)04456-6
Keywords: Immersed surface, self-intersection set, daisy graph
Received by editor(s): October 15, 1996
Received by editor(s) in revised form: April 7, 1997
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 1998 American Mathematical Society