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Circle immersions that can be divided into two arc embeddings
Author(s):
Kouki
Taniyama
Journal:
Proc. Amer. Math. Soc.
138
(2010),
743-751.
MSC (2000):
Primary 57M99;
Secondary 57M25, 57M27
Posted:
October 1, 2009
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Abstract:
We give a complete characterization of a circle immersion that can be divided into two arc embeddings in terms of its chord diagram.
References:
-
- 1.
- C. Adams, R. Shinjo and K. Tanaka, Complementary regions of knot and link diagrams, arXiv:0812.2558 (2008).
- 2.
- T. Hagge, to appear.
- 3.
- G. Hotz, Arkadenfadendarstellung von Knoten und eine neue Darstellung der Knotengruppe (German), Abh. Math. Sem. Univ. Hamburg, 24 (1960), 132-148. MR 0111047 (22:1912)
- 4.
- M. Ozawa, Edge number of knots and links, arXiv:0705.4348 (2007).
- 5.
- R. Shinjo, Complementary regions of projections of spatial graphs, in preparation.
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Additional Information:
Kouki
Taniyama
Affiliation:
Department of Mathematics, School of Education, Waseda University, Nishi-Waseda 1-6-1, Shinjuku-ku, Tokyo, 169-8050, Japan
Email:
taniyama@waseda.jp
DOI:
10.1090/S0002-9939-09-10140-5
PII:
S 0002-9939(09)10140-5
Keywords:
Circle immersion,
chord diagram,
plane curve,
knot projection
Received by editor(s):
February 9, 2009,
Received by editor(s) in revised form:
April 2, 2009
Posted:
October 1, 2009
Additional Notes:
The author was partially supported by Grant-in-Aid for Scientific Research (C) (No. 18540101), Japan Society for the Promotion of Science.
Communicated by:
Alexander N. Dranishnikov
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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