Different links with the same Links-Gould invariant
Ishii, Atsushi ; Kanenobu, Taizo
Osaka J. Math., Tome 42 (2005) no. 1, p. 273-290 / Harvested from Project Euclid
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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.
Publié le : 2005-06-14
Classification:  
@article{1153494378,
     author = {Ishii, Atsushi and Kanenobu, Taizo},
     title = {Different links with the same Links-Gould invariant},
     journal = {Osaka J. Math.},
     volume = {42},
     number = {1},
     year = {2005},
     pages = { 273-290},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1153494378}
}

Ishii, Atsushi; Kanenobu, Taizo. Different links with the same Links-Gould invariant. Osaka J. Math., Tome 42 (2005) no. 1, pp.  273-290. http://gdmltest.u-ga.fr/item/1153494378/