Topological Classification of Real Three-Dimensional Cubics

The paper is devoted to finding topological types of nonsingular real three-dimensional cubics. It is proved that the following topological types exist: the projective space, the disjoint union of the projective space and the sphere, the projective space with handles whose number can vary from one to five. Along with these types, there is another topological type which is possibly distinct from those listed above, and this type is yet not completely described. A real cubic of this type is obtained from the projective space by replacing some solid torus in the space by another solid torus such that, under this replacement, the meridians of the first solid torus become parallels of the other solid torus, and conversely.