Algebraic structure of the space of homotopy classes of cycles and singular homology

Valery Dolotin

Published 2003-01-06Version 1

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 $\pi_k(M)$.