Knot theory and cluster algebras

We establish a connection between knot theory and cluster algebras via representation theory. To every diagram (or link diagram), we associate algebra by constructing quiver with potential. The rank of the is 2n, where n number crossing points in diagram. then construct 2n indecomposable modules T(i) over Jacobian For each T(i), show that submodule lattice isomorphic to corresponding Kauffman states. give realization Alexander polynomial as specialization F-polynomial for i. Furthermore, conjecture collection forms whose opposite initial quiver, resulting automorphism order two.