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 cy- cle length of link. Also, we give bounds of Gordian distance between the (p; q)-torus knot and the closure of a braid of two specic quasitoric braids which are called an alternating quasitoric braid and a blockwise alternat- ing 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 10139 and 10124, we can prove that u(10139) = 4 and d ×(10124;K(3; 13)) = 8.
Original language | English |
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Pages (from-to) | 1305-1321 |
Number of pages | 17 |
Journal | Journal of the Korean Mathematical Society |
Volume | 52 |
Issue number | 6 |
DOIs | |
State | Published - 2015 |
Keywords
- Braid
- Braid index
- Knot
- Link
- Qua-sitoric braid index
- Quasitoric braid
- Toric braid