On the Uniqueness of Sarkar-Seed-Szabo Construction

Abstract

In an attempt to consolidate Szabo's geometric chain complex and Bar\hyp Natan's chain complex, Sarkar-Seed-Szabo defined a total complex $CTot(L)$ over ${\mathbb{F}}_2$ by adding some extra terms $\{h_i{\}}_{i=2}^{\infty }$ in the differential. In this paper we prove the uniqueness of $\{h_i{\}}_{i=2}^{\infty }$ upto some properties. This in turn implies that the total complex $CTot(L)$ is unique.