Khovanov multicurves are linear

Abstract

In previous work we introduced a Khovanov multicurve invariant $\widetilde{\mathrm{Kh}}$ associated with Conway tangles. Applying ideas from homological mirror symmetry we show that $\widetilde{\mathrm{Kh}}$ is subject to strong geography restrictions: Every component of the invariant is linear, in the sense that it admits a lift to a curve homotopic to a straight line in an appropriate planar cover of the tangle boundary.

41 pages, many colour figures. The contents of this paper used to be part of arXiv:2105.06308