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A Colored Khovanov Homotopy Type And Its Tail For B-Adequate Links (1602.03856v2)
Published 11 Feb 2016 in math.GT
Abstract: We define a Khovanov homotopy type for $sl_2(\mathbb{C})$ colored links and quantum spin networks and derive some of its basic properties. In the case of $n$-colored B-adequate links, we show a stabilization of the homotopy types as the coloring $n\rightarrow\infty$, generalizing the tail behavior of the colored Jones polynomial. Finally, we also provide an alternative, simpler stabilization in the case of the colored unknot.