The space of 3-manifolds

In this paper we develop the theory of finite-type invariants for homologic ally nontrivial 3-manifolds. We construct an infinite-dimensional Euclidean space with a hypersurface in it corresponding to manifolds with Morse sing ularities. The connected components of the complement to the discriminant c orrespond to homeomorphism classes of spin 3-manifolds. We give the definit ion of the invariant of finite type, suggested by the geometry of the space and give an example or the invariant of order 1. (C) 2000 Academie des sci ences/Editions scientifiques et medicales Elsevier SAS.