  Described the algebraic structure on the space of homotopy classes of cycles
with marked topological flags of disks. This space is a non-commutative monoid,
with an Abelian quotient corresponding to the group of singular homologies
$H_k(M)$. For the marked flag contracted to a point the multiplication becomes
commutative and the subgroup of spherical cycles corresponds to the usual
homotopy group $\pi_k(M)$.

Algebraic Topology;K-Theory and Homology