ON THE QUASITORIC BRAID INDEX OF A LINK

Title & Authors
ON THE QUASITORIC BRAID INDEX OF A LINK
BAE, YONGJU; SEO, SEOGMAN;

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 $\small{10_{139}}$ and $\small{10_{124}}$, we can prove that $\small{u(10_{139})=4}$ and $\small{d^{\times}(10_{124},K(3,13))=8}$.
Keywords
link;knot;braid;toric braid;quasitoric braid;braid index;quasitoric braid index;
Language
English
Cited by
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