On the uniqueness of Sarkar-Seed-Szabo construction

Abstract

In an attempt to consolidate Szabo’s geometric chain complex and Bar Natan’s chain complex, Sarkar–Seed–Szabo defined a total complex [Formula: see text] over [Formula: see text] by adding some extra terms [Formula: see text] in the differential for a link diagram [Formula: see text] of [Formula: see text] in [Formula: see text]. In this paper, we prove the uniqueness of [Formula: see text] upto some properties. This in turn implies that the total complex [Formula: see text] is unique.