A colored Khovanov spectrum and its tail for B–adequate links

Willis, Michael

doi:10.2140/agt.2018.18.1411

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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

DOI: 10.2140/agt.2018.18.1411

Abstract

We define a Khovanov spectrum for ${𝔰 𝔩}_{2} (ℂ)$ –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 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.

Keywords

Khovanov spectrum, Khovanov stable homotopy type, colored Khovanov homology

Mathematical Subject Classification 2010

Primary: 57M27, 57M25

References

Publication

Received: 8 August 2016

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

Volume 18, issue 3 (2018)