Annular Khovanov homology and meridional disks

Gage Martin (Boston College)

Abstract: The wrapping conjecture of Hoste-Przytycki suggests a relationship between the maximum non-zero annular Khovanov grading and the minimal geometric intersection number with a meridional disk. Inspired by this conjecture, we exhibit infinite families of annular links for which the maximum non-zero annular Khovanov grading grows infinitely large but the maximum non-zero annular Floer-theoretic gradings are bounded. We also show this phenomenon exists at the decategorified level for some of the infinite families. Our computations provide further evidence for the wrapping conjecture and its categorified analogue. Additionally, we show that certain satellite operations cannot be used to construct counterexamples to the categorified wrapping conjecture.