On the Colored HOMFLY-PT, Multivariable and Kashaev Link Invariants

Nathan Geer , Bertrand Patureau-Mirand (1)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

We study various specializations of the colored HOMFLY-PT polynomial. These specializations are used to show that the multivariable link invariants arising from a complex family of sl(m|n) super-modules previously defined by the authors contains both the multivariable Alexander polynomial and Kashaev's invariants. We conjecture these multivariable link invariants also specialize to the generalized multivariable Alexander invariants defined by Y. Akutsu, T. Deguchi, and T. Ohtsuki.

Domaines: Topologie géométrique [math.GT]; Algèbres quantiques [math.QA]

Nathan Geer, Bertrand Patureau-Mirand. On the Colored HOMFLY-PT, Multivariable and Kashaev Link Invariants. Communications in Contemporary Mathematics, 2008, pp.10, 993. ⟨10.1142/S0219199708003125⟩. ⟨hal-00430466⟩