Browse > Article
http://dx.doi.org/10.5666/KMJ.2017.57.2.331

On Minimal Unknotting Crossing Data for Closed Toric Braids  

Siwach, Vikash (Department of Mathematics, Indian Institute of Technology Ropar)
Prabhakar, Madeti (Department of Mathematics, Indian Institute of Technology Ropar)
Publication Information
Kyungpook Mathematical Journal / v.57, no.2, 2017 , pp. 331-360 More about this Journal
Abstract
Unknotting numbers for torus knots and links are well known. In this paper, we present a new approach to determine the position of unknotting number crossing changes in a toric braid such that the closure of the resultant braid is equivalent to the trivial knot or link. Further we give unknotting numbers of more than 600 knots.
Keywords
torus Knots; unknotting Number; braids;
Citations & Related Records
연도 인용수 순위
  • Reference
1 S. Bleiler, A note on unknotting number, Math. Proc. Cambridge Philos. Soc., 96(1984), 469-471.   DOI
2 J. Hoste, M. Thistlethwaite, and J. Weeks, The first 1,701,936 knots, Math. Intelligencer, 20(1998), 33-48.   DOI
3 J. Hoste, M. Thistlethwaite, and J. Weeks, Knotscape, 1999.
4 S. Jablan and R. Sazdanovic. Linknot-knot theory by computer, Series on Knots and Everything 21, World Scientific, Singapore.
5 P. Kronheimer and T. Mrowka, Gauge theory for embedded surfaces, I, Topology, 32(1993), 773-826.   DOI
6 P. Kronheimer and T. Mrowka, Gauge theory for embedded surfaces, II, Topology, 34(1995), 37-97.   DOI
7 Y. Nakanishi, Unknotting numbers and knot diagrams with the minimum crossings, Math. Sem. Notes Kobe Univ., 11(1983), 257-258.
8 V. Siwach and P. Madeti, A sharp upper bound for region unknotting number of torus knots, J. Knot Theory Ramifications, 22(5)(2013), 1350019, 21 pages.   DOI
9 V. Siwach and P. Madeti, An unknotting sequence for torus knots, Topology Appl., 196(B)(2015) 668-674.   DOI