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ON THE PRESENTATION OF A LINK AS A SUM OF TWO DESCENDING TANGLE DIAGRAMS

YONGJU BAE

Department of Mathematics, Kyungpook National University, Daegu 702-701, Korea

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MYOUNGSOO SEO

Department of Mathematics, Kyungpook National University, Daegu 702-701, Korea

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https://doi.org/10.1142/S0218216513500703Cited by:0 (Source: Crossref)

Abstract

In this paper, we define the notion of descending tangle diagrams and give a presentation of a link as a sum of two descending tangle diagrams. We also introduce a new invariant of links and find its basic properties.

Keywords:

AMSC: 57M25

References

J. W. Alexander, Proc. Natl. Acad. Sci. USA 9, 93 (1923), DOI: 10.1073/pnas.9.3.93. Crossref, Google Scholar
E. Artin, Abh. Math. Semin. Univ. Hamb. 4, 47 (1925), DOI: 10.1007/BF02950718. Crossref, Google Scholar
Y. Bae and C.-Y. Park, Math. Proc. Cambridge Philos. Soc. 129, 491 (2000), DOI: 10.1017/S0305004100004576. Crossref, Web of Science, Google Scholar
J. S. Birman and W. W. Menasco, Topology 33, 525 (1994), DOI: 10.1016/0040-9383(94)90027-2. Crossref, Web of Science, Google Scholar
P. R. Cromwell, Topol. Appl. 64, 37 (1995), DOI: 10.1016/0166-8641(94)00087-J. Crossref, Web of Science, Google Scholar
P. R. Cromwell , Knots and Links ( Cambridge University Press , Cambridge , 2004 ) . Crossref, Google Scholar
P. R. Cromwell and I. J. Nutt, Math. Proc. Cambridge Philos. Soc. 119, 309 (1996), DOI: 10.1017/S0305004100074181. Crossref, Web of Science, Google Scholar
J. Franks and R. F. Williams, Trans. Amer. Math. Soc. 303, 97 (1987), DOI: 10.1090/S0002-9947-1987-0896009-2. Crossref, Web of Science, Google Scholar
Y. Huh and S. Oh, J. Knot Theory Ramifications 20, 741 (2011), DOI: 10.1142/S0218216511008966. Link, Web of Science, Google Scholar
G. T. Jin and W. K. Park, J. Knot Theory Ramifications 19, 1655 (2010), DOI: 10.1142/S0218216510008595. Link, Web of Science, Google Scholar
H. R. Morton, Math. Proc. Cambridge Philos. Soc. 99, 107 (1986), DOI: 10.1017/S0305004100063982. Crossref, Web of Science, Google Scholar
H. R. Morton and E. Beltrami, Math. Proc. Cambridge Philos. Soc. 123, 41 (1998), DOI: 10.1017/S0305004197002090. Crossref, Web of Science, Google Scholar
K. Murasugi, Trans. Amer. Math. Soc. 326, 237 (1991), DOI: 10.1090/S0002-9947-1991-1000333-3. Crossref, Web of Science, Google Scholar
L. Ng, J. Knot Theory Ramifications 21, 1250031 (2012), DOI: 10.1142/S0218216511009820. Link, Web of Science, Google Scholar
C.-Y. Park and M. Seo, Bull. Aust. Math. Soc. 61, 177 (2000), DOI: 10.1017/S0004972700022188. Crossref, Web of Science, Google Scholar

Vol. 22, No. 11

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History

Received 21 May 2013

Accepted 15 October 2013

Published: 22 November 2013

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ON THE PRESENTATION OF A LINK AS A SUM OF TWO DESCENDING TANGLE DIAGRAMS

Abstract

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