A perturbation of the geometric spectral sequence in Khovanov homology

TL;DR

This paper explores the connection between two perturbations in Khovanov homology, introduces a unified link invariant, and develops a family of s-invariants inspired by Rasmussen's work.

Contribution

It constructs a new link invariant that generalizes Bar-Natan's and Szabo's perturbations and introduces a novel family of s-invariants within this framework.

Findings

Established a relationship between Bar-Natan's perturbation and Szabo's spectral sequence

Constructed a new, unified link invariant combining both perturbations

Proposed a family of s-invariants derived from the new theory

Abstract

We study the relationship between Bar-Natan's perturbation in Khovanov homology and Szabo'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.