A colored Khovanov spectrum and its tail for $\mathit{B}$–adequate links

Abstract

We define a Khovanov spectrum for ${\mathfrak{s}\mathfrak{l}}_2\left(ℂ\right)$–colored links and quantum spin networks and derive some of its basic properties. In the case of $n$–colored $\mathit{B}$–adequate links, we show a stabilization of the spectra as the coloring $n\to \infty$, generalizing the tail behavior of the colored Jones polynomial. Finally, we also provide an alternative, simpler stabilization in the case of the colored unknot.