No Access

NON-CONJUGATE BRAIDS WHOSE CLOSURES RESULT IN THE SAME KNOT

REIKO SHINJO

Osaka City University Advanced Mathematical Institute, 3-138 Sugimoto 3-chome, Sumiyoshi-ku, Osaka 558-8585, Japan

https://doi.org/10.1142/S0218216510007735Cited by:5 (Source: Crossref)

Abstract

For any knot K represented as an n-braid (n ≥ 3), we construct an infinite sequence of pairwise non-conjugate (n + 1)-braids {b_m, m ∈ ℕ} representing K.

Keywords:

AMSC: 57M25, 57M27, 20F36

References

E. Artin, Ann. Math. 48, 101 (1947), DOI: 10.2307/1969218. Crossref, Web of Science, Google Scholar
J. S. Birman and W. W. Menasco, Pacific J. Math. 156(2), 265 (1992). Crossref, Web of Science, Google Scholar
J. S. Birman and W. W. Menasco, Pacific J. Math. 161(1), 25 (1993). Crossref, Web of Science, Google Scholar
T. Fiedler, Topology 32(2), 281 (1993), DOI: 10.1016/0040-9383(93)90020-V. Crossref, Web of Science, Google Scholar
E. Fukunaga , Topology of Knots V ( Waseda University , 2002 ) . Google Scholar
E. Fukunaga, An infinite sequence of conjugacy classes in the 4-braid group representing a torus link of type (2, k), preprint . Google Scholar
F. Garside, Q. J. Math. Oxford 20, 235 (1969), DOI: 10.1093/qmath/20.1.235. Crossref, Web of Science, Google Scholar
J. Hoste, Proc. Amer. Math. Soc. 95(2), 299 (1985), DOI: 10.2307/2044531. Crossref, Web of Science, Google Scholar
T. Kanenobu and Ryo Nikkuni, Topol. Appl. 147, 91 (2005). Google Scholar
H. R. Morton, Topology 17(1), 101 (1978), DOI: 10.1016/0040-9383(78)90016-2. Crossref, Web of Science, Google Scholar
H. R. Morton, Math. Proc. Cambridge Philos. Soc. 93(2), 259 (1983), DOI: 10.1017/S0305004100060540. Crossref, Web of Science, Google Scholar
H. Murakami and Y. Nakanishi, Math. Ann. 284, 75 (1989), DOI: 10.1007/BF01443506. Crossref, Web of Science, Google Scholar
R. Shinjo, Intelligence of Low Dimensional Topology 2006, Series on Knots and Everything 40 (World Scientific Publishing, 2007) pp. 293–297. Link, Google Scholar
A. Stoimenow, Lie groups, Burau representation, and non-conjugate braids with the same closure link, preprint . Google Scholar