On self-intersections of immersed surfaces

Author:
Gui-Song Li

Journal:
Proc. Amer. Math. Soc. **126** (1998), 3721-3726

MSC (1991):
Primary 57M42

DOI:
https://doi.org/10.1090/S0002-9939-98-04456-6

MathSciNet review:
1459134

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-98-04456-6

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