Quantum SU(3) Invariant of 3-Manifolds via Linear Skein Theory

The linear skein theory for the Kauffman bracket was introduced by Lickorish [11,12]. It gives an elementary construction of quantum SU(2) invariant of 3-manifolds. In this paper we prove basic properties of the linear skein theory for quantum SU(3) invariant. By using them we give an elementary construction of quantum SU(3) invariant of 3-manifolds and prove topological invariance of the invariant along the construction.