Volume 18, issue 3 (2018)

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

Michael Willis

Algebraic & Geometric Topology 18 (2018) 1411–1459

We define a Khovanov spectrum for 𝔰𝔩2()–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 spectra as the coloring n , generalizing the tail behavior of the colored Jones polynomial. Finally, we also provide an alternative, simpler stabilization in the case of the colored unknot.

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Khovanov spectrum, Khovanov stable homotopy type, colored Khovanov homology
Mathematical Subject Classification 2010
Primary: 57M27, 57M25
Received: 8 August 2016
Revised: 20 January 2017
Accepted: 28 February 2017
Published: 3 April 2018
Michael Willis
Department of Mathematics
University of Virginia
Charlottesville, VA
United States