The adjacency graph of a real algebraic surface

The paper deals with the question of recognizing the mutual positions of the connected components of a non-singular real projective surface S in the real projective 3-space.We present an algorithm that answers this question through the computation of the adjacency graph of the surface; it also allows to decide whether each connected component is contractible or not. The algorithm, combined with a previous one returning as an output the topology of the surface, computes a set of data invariant up to ambient-homeomorphism which, though not sufficient to determine the pair (RP3, S), give information about the nature of the surface as an embedded object