NON SEMI-SIMPLE sl(2) QUANTUM INVARIANTS, SPIN CASE

Abstract. Invariants of 3-manifolds from a non semi-simple category of modules over a version of quantum sl(2) were obtained by the last three authors in [8]. In their construction the quantum parameter q is a root of unity of order 2r where r> 1 is odd or congruent to 2 modulo 4. In this paper we consider the remaining cases where r is congruent to zero modulo 4 and produce invariants of 3-manifolds with colored links, equipped with generalized spin structure. For a given 3-manifold M, the relevant generalized spin structures are (non canonically) parametrized by H1(M;C/2Z)