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

 

Circle immersions that can be divided into two arc embeddings


Author: Kouki Taniyama
Journal: Proc. Amer. Math. Soc. 138 (2010), 743-751
MSC (2000): Primary 57M99; Secondary 57M25, 57M27
Published electronically: October 1, 2009
MathSciNet review: 2557191
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Abstract | References | Similar Articles | Additional Information

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

  • 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. Günter Hotz, Arkadenfadendarstellung von Knoten und eine neue Darstellung der Knotengruppe, Abh. Math. Sem. Univ. Hamburg 24 (1960), 132–148 (German). 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: http://dx.doi.org/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
Published electronically: 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
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.