ON THE QUASITORIC BRAID INDEX OF A LINK

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 $10_{139}$ and $10_{124}$, we can prove that $u(10_{139})=4$ and $d^{\times}(10_{124},K(3,13))=8$.