ИСТИНА

The Euler characteristic is the only additive topological invariant for spaces of certain sort, in particular, for manifolds with some finiteness properties. A generalization of the notion of a manifold is the notion of a (real) orbifold called sometimes a V-manifold. We discuss a universal additive topological invariant of orbifolds: the universal Euler characteristic. It takes values in the ring R freely generated (as a Z-module) by the isomorphism classes of finite groups. The ring R is the polynomial ring in the variables corresponding to the indecomposable finite groups. We also consider the universal Euler characteristic on the class of locally closed equivariant unions of cells in equivariant CW-complexes. We show that it is a universal additive invariant satisfying a certain "induction relation". We give Macdonald type equations for the universal Euler characteristic for orbifolds and for cell complexes of the described type. The talk is based on a joint work with I.Luengo and A.Melle-Hernandez (Complutense University of Madrid). The work was supported by the RSF grant 16-11-10018.