Normal surfaces and colored Khovanov homology
arXiv:2201.13393
Abstract
We show that colored Khovanov homology detects classes of essential surfaces as a direct analogue of the slope conjectures for the colored Jones polynomial. We do this by identifying certain generators of the colored Khovanov chain complex with normal surfaces in the complement of the knot using an ideal triangulation from a diagram.
26 pages, 26 figures