2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150844In this paper we develop the theory of finite-type invariants for homologically nontrivial 3-manifolds. We construct an infinite-dimensional affine space with a hypersurface in it corresponding to manifolds with Morse singularities. Connected components of the complement of this hypersurface correspond to homeomorphism type of spin 3-manifolds. This suggests the natural axiomatics of Vassiliev finite-type invariants for arbitrary closed 3-manifolds. An example of an invariant of order 1 is given.9 pages, plain TEXQuantum Algebratext