ON THE QUASITORIC BRAID INDEX OF A LINK
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We de ne 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 specific quasitoric braids which are called an alternating quasitoric braid and a blockwise alternat- ing quasitoric braid. We give a method of modi cation 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.
Abstract
We de ne 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 specific quasitoric braids which are called an alternating quasitoric braid and a blockwise alternat- ing quasitoric braid. We give a method of modi cation 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.
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