A perturbation of the geometric spectral sequence in Khovanov homology

Abstract

We study the relationship between Bar-Natan’s perturbation in Khovanov homology and Szabó’s geometric spectral sequence, and construct a link invariant that generalizes both into a common theory. We study a few properties of the new invariant, and introduce a family of $s$-invariants from the new theory in the same spirit as Rasmussen’s $s$-invariant.