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ASCENDING NUMBER OF KNOTS AND LINKS

MAKOTO OZAWA

Department of Natural Sciences, Faculty of Arts and Sciences, Komazawa University, 1-23-1 Komazawa, Setagaya-ku, Tokyo 154-8525, Japan

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https://doi.org/10.1142/S0218216510007723Cited by:15 (Source: Crossref)

Abstract

We introduce a new numerical invariant of knots and links from the descending diagrams. It is considered to live between the unknotting number and the bridge number. Some fundamental results and an incomplete table of the invariant for knots with 8-crossings or less are given.

Keywords:

AMSC: 57M25

References

C. Adams , The Knot Book ( American Mathematical Society , 2004 ) . Google Scholar
G. Burde and H. Zieschang , Knots ( Walter de Gruyter , 2002 ) . Crossref, Google Scholar
P. Cromwell , Knots and Links ( Cambridge University Press , 2004 ) . Crossref, Google Scholar
S. Fujimura, On the ascending number of knots, a thesis, Hiroshima University (1998) . Google Scholar
A. Kawauchi , Survey on Knot Theory ( Birkhäuser Verlag , 1996 ) . Google Scholar
R. Kirby, Geometric Topology 2 (American Mathematical Society, 1997) pp. 35–473. Google Scholar
P. B. Kronheimer and T. S. Mrowka, Topology 32, 773 (1993), DOI: 10.1016/0040-9383(93)90051-V. Crossref, Web of Science, Google Scholar
W. B. R. Lickorish, Contemp. Math. 44, 117 (1985). Crossref, Google Scholar
W. B. R. Lickorish , An Introduction to Knot Theory ( Springer , 1997 ) . Crossref, Google Scholar
C. Livingston , Knot Theory ( The Mathematical Association of America , 1996 ) . Google Scholar
B. Kurpita K. Murasugi , Knot Theory and Its Applications ( Birkhäuser , Boston , 1996 ) . Google Scholar
M. Okuda, A determination of the ascending number of some knots, a thesis, Hiroshima University (1998) . Google Scholar
M. Ozawa, Ascending number of knots and links, a talk in a conference "Knot Theory" at Waseda University (1995) . Google Scholar
P. Ozsvath and Z. Szabo, Topology 44, 705 (2005), DOI: 10.1016/j.top.2005.01.002. Crossref, Google Scholar
D. Rolfsen , Knots and Links ( AMS Chelsea Publishing , 2003 ) . Crossref, Google Scholar
H. Schubert, Math. Z. 61, 245 (1954), DOI: 10.1007/BF01181346. Crossref, Google Scholar
A. Stoimenow, Compositio Math. 140, 228 (2004), DOI: 10.1112/S0010437X03000174. Crossref, Web of Science, Google Scholar
S. Suzuki , An Introduction to Knot Theory ( Saiensu-sha Co., Ltd. Publishers , 1991 ) . Google Scholar