We discuss some approaches to the topological study of real quadratic mappings. Two effective methods of computing the Euler characteristics of fibers are presented which enable one to obtain comprehensive results for quadratic mappings with two-dimensional fibers. As an illustration we obtain a complete topological classification of configuration spaces of planar pentagons.

A classification of simple equivalence classes of function germs with respect to new relations is given. The equivalence relation is similar but weaker than the right action of diffeomorphisms which preserve the boundary. It is used in classifying Lagrange projections with boundary. The simple classes of function germs with respect to the equivalence similar to fibration preserving action are also discussed.

Nous considérons les groupes de cobordisme (définis par Arnold) d’immersions lagrangiennes exactes de variétés compactes dans ${\mathbf{R}}^{2n}$. Grâce au théorème de Gromov-Lees, leur calcul est celui des groupes d’homotopie de spectres de Thom construits sur les espaces $U/O$ (cas non-orienté, le calcul est alors dû à Smith et Stong) et $U/SO$ (cas orienté, groupes dont nous calculons la “partie paire”, et sur la “partie impaire” desquels nous donnons des informations). Nous calculons aussi les images de ces groupes dans...