JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ON THE QUASITORIC BRAID INDEX OF A LINK
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
ON THE QUASITORIC BRAID INDEX OF A LINK
BAE, YONGJU; SEO, SEOGMAN;
  PDF(new window)
 Abstract
We dene new link invariants which are called the quasitoric braid index and the cyclic length of a link and show that the quasitoric braid index of link with k components is the product of k and the cycle length of link. Also, we give bounds of Gordian distance between the (p,q)-torus knot and the closure of a braid of two specific quasitoric braids which are called an alternating quasitoric braid and a blockwise alternating quasitoric braid. We give a method of modication which makes a quasitoric presentation from its braid presentation for a knot with braid index 3. By using a quasitoric presentation of and , we can prove that and .
 Keywords
link;knot;braid;toric braid;quasitoric braid;braid index;quasitoric braid index;
 Language
English
 Cited by
 References
1.
C. Adams, The Knot Book, W. H. Freeman and Company, 1994.

2.
E. Artin, Theory of braids, Ann. of Math. (2) 48 (1947), 101-126. crossref(new window)

3.
W. Gibson and M. Ishikawa, Links and Gordian numbers associated with generic immersions of intervals, Topology Appl. 123 (2002), no. 3, 609-636. crossref(new window)

4.
C. McA. Gordon, R. A. Litherland, and K. Murasugi, Signatures of covering links, Canad. J. Math. 33 (1981), no. 2, 381-394. crossref(new window)

5.
A. Kawauchi, Distance between links by zero-linking twists, Kobe J. Math. 13 (1996), no. 2, 183-190.

6.
P. Kronheimer and T. Mrowka, Gauge theory for embedded surfaces I, Topology 32 (1993), no. 4, 773-826. crossref(new window)

7.
P. Kronheimer and T. Mrowka, Gauge theory for embedded surfaces II, Topology 34 (1995), no. 1, 37-97. crossref(new window)

8.
V. O. Manturov, A combinatorial representation of links by quasitoric braids, European J. Combin. 23 (2002), no. 2, 207-212. crossref(new window)

9.
K. Murasugi and B. Kurpita, A Study of Braids, Kluwer Academic Publishers, 1999.

10.
Y. Ohyama, On the Minimal Crossing Number and the Braid Index of Links, Canad. J. Math. 45 (1993), no. 1, 117-131. crossref(new window)

11.
K. Taniyama, Unknotting numbers of diagrams of a given nontrivial knot are unbounded, J. Knot Theory Rami cations 18 (2009), no. 8, 1049-1063.