Computations of Szab\'o's Geometric Spectral Sequence in Khovanov Homology

TL;DR

This paper details the computation of Szabó's geometric spectral sequence in Khovanov homology, providing new insights and conjectures about its structure based on extensive computational results.

Contribution

It introduces a methodology for computing Szabó's spectral sequence and presents new conjectures and propositions about its structure based on computational data.

Findings

Computed Szabó's spectral sequence for various cases

Formulated conjectures on the spectral sequence's structure

Proved propositions supporting the conjectures

Abstract

Szab\'o recently introduced a combinatorially-defined spectral sequence in Khovanov homology. After reviewing its construction and explaining our methodology for computing it, we present results of computations of the spectral sequence. Based on these computations, we make a number of conjectures concerning the structure of the spectral sequence, and towards those conjectures, we prove some propositions.