On a family of topological invariants similar to homotopy groups

Abstract

Summary.- The intimacy relation between smooth loops, which is a strong homotopy relation, is generalized to smooth maps dened on the n-cube, leading to a family of groups similar to the clas-sical homotopy groups. The formal resemblance between the two families of groups is explored. Special attention is devoted to the role of these groups as topological invariants for manifolds and as tools for describing geometrical structures dened on manifolds such as bundles and connections. 1.