Computing Khovanov homology of tangles

Abstract

The computation of Khovanov homology for tangles has significant potential applications, yet explicit computational studies remain limited. In this work, we present a method for computing the Khovanov homology of tangles via an arc reduction approach, and we derive the Poincar\'e polynomial for simple tangles. Furthermore, we compute the Poincar\'e polynomials of tangles with at most three crossings.