Some new examples of links with the same polynomials

Abstract

We call a link (knot) [Formula: see text] to be strongly Jones (respectively, Homfly) undetectable, if there are infinitely many links which are not isotopic to [Formula: see text] but share the same Jones (respectively, Homfly) polynomial as [Formula: see text]. We reconstruct Kanenobu’s knot [Kanenobu, Infinitely many knots with the same polynomial invariant, Proc. Amer. Math. Soc. 97(1) (1986), 158–162] and give two new constructions. Using these constructions, we give some examples of strongly Jones undetectable: [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] ([Formula: see text] is the mirror image of [Formula: see text]) and etc. For some special cases, these constructions will be shown to be strongly Jones undetectable and strongly Homfly undetectable.