Order of a Function on the Bruschlinsky Group

Abstract

For an arbitrary function F defined on the group of homotopy classes of mappings of a finite polyhedron X to the circle and taking values in an Abelian group Q, the notion of order is defined. The order ord F is compared with the algebraic degree of F. It is proved that ord F⩽deg F and deg F⩽dim X • ord F. The inequality ord F⩾deg F is proved in the case where Q is torsion-free or ord F⩽1. Bibliography: 2 titles.