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June 2005 Different links with the same Links-Gould invariant
Atsushi Ishii, Taizo Kanenobu
Osaka J. Math. 42(2): 273-290 (June 2005).


Using the skein relations for the Links-Gould (LG) invariant discovered by the first author, we give two constructions to provide a pair of different knots or links sharing the same LG invariant. Using this, we give examples of arbitrarily many 2-bridge knots with the same LG invariant. These knots also share the same HOMFLY and Kauffman polynomials. Further, for 2-bridge links we construct a similar example, which also share the same 2-variable Alexander polynomial. We also give a non-amphicheiral hyperbolic knot whose chirality is not undetected by the LG invariant.


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Atsushi Ishii. Taizo Kanenobu. "Different links with the same Links-Gould invariant." Osaka J. Math. 42 (2) 273 - 290, June 2005.


Published: June 2005
First available in Project Euclid: 21 July 2006

zbMATH: 1082.57004
MathSciNet: MR2147736

Rights: Copyright © 2005 Osaka University and Osaka City University, Departments of Mathematics


Vol.42 • No. 2 • June 2005
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