Resumen: Two smooth, oriented, closed manifolds M and N are cut-and-paste equivalent if one can obtain N by a series of cut-and-paste operations from M. Cut-and-paste controlled invariants (SKK invariants) are functions on the set of smooth manifolds whose values on cut-and-paste equivalent manifolds differ by an error term depending only on the gluing diffeomorphisms. The relation between SKK invariant and invertible TQFTs was first investigated by Kreck, Stolz, and Teichner. In this talk, I will present the construction of a group homomorphism between the group of invertible TQFTs and the group of SKK invariants and describe how these groups fit into a split exact sequence.