A Kirby color for Khovanov homology

Matthew Hogancamp; David E. V. Rose; Paul Wedrich

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arXiv · 2210.05640

A Kirby color for Khovanov homology

Matthew Hogancamp·David E. V. Rose·Paul Wedrich

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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 $\mathfrak{gl}_{2}$ skein lasagna module, hence is an invariant of $4$-dimensional $2$-handlebodies.

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BibTeX RIS

Matthew Hogancamp, David E. V. Rose, Paul Wedrich. 2022-10-11. A Kirby color for Khovanov homology. https://arxiv.org/abs/2210.05640

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