Stable classification of 4-manifolds obtained by the surgery on loops

This paper is concerned with the problem of stable diffeomorphism classification of 4-manifolds obtained using the surgery on loops. The main theorem states that under the assumption that the normal 1-type of two 4-manifolds in question is the same, the only classifying invariant is the signature. In particular, in some cases, any two closed smooth 4-manifolds with a given fundamental group, obtained by the standard construction, are stably diffeomorphic.