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
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.

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