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A Kirby color for Khovanov homology

  • Matthew Hogancamp

    Northeastern University, Boston, USA

  • David E. V. Rose

    University of North Carolina at Chapel Hill, Chapel Hill, USA

  • Paul Wedrich

    Universität Hamburg, Hamburg, Germany
A Kirby color for Khovanov homology cover
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Abstract

We construct a Kirby color in the setting of Khovanov homology: an ind-object of the annular Bar-Natan category that is equipped with a natural handle slide isomorphism. Using functoriality and cabling properties of Khovanov homology, we define a Kirby-colored Khovanov homology that is invariant under the handle slide Kirby move, up to isomorphism. Via the Manolescu–Neithalath 2-handle formula, Kirby-colored Khovanov homology agrees with the skein lasagna module, hence is an invariant of 4-dimensional 2-handlebodies.

Cite this article

Matthew Hogancamp, David E. V. Rose, Paul Wedrich, A Kirby color for Khovanov homology. J. Eur. Math. Soc. (2025), published online first

DOI 10.4171/JEMS/1589