The stabilized-unknot formula for the annular Khovanov invariant

Let σnϵnσn1ϵn1σ1ϵ1\sigma_n^{\epsilon_n}\sigma_{n-1}^{\epsilon_{n-1}}\cdots\sigma_1^{\epsilon_1} be a stabilized unknot, where each ϵi=±1\epsilon_i=\pm1, and let W0W_0 denote the corresponding invariant in the annular Khovanov decomposition. Stabilized-unknot conjecture. Its graded dimension is

dimW0=zϵi(qz+q1z1).\dim W_0=z^{-\sum \epsilon_i}(qz+q^{-1}z^{-1}).

This is a conjectural formula for the annular grading of stabilized unknots; the supplied text gives no resolution or further evidence about its status.

Sources & referencesView supporting material

Primary source

Hilary Hunt, Hannah Keese, Anthony Licata and Scott Morrison, “Computing annular Khovanov homology”, arXiv:1505.04484 (2015).

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