Geodesic
Algebraic Structure of the Space of Homotopy Classes of Cycles and Singular Homology
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 142-146.

Voir la notice de l'article provenant de la source Math-Net.Ru

The algebraic structure on the space of homotopy classes of cycles with marked topological flags of disks is described. This space is a noncommutative monoid, with an abelian quotient corresponding to the group of singular homologies $H_k(M)$. For a marked flag contracted to a point, the multiplication becomes commutative, and the subgroup of spherical cycles corresponds to the usual homotopy group $\pi_k(M)$. 
@article{TM_2004_246_a8,
     author = {V. V. Dolotin},
     title = {Algebraic {Structure} of the {Space} of {Homotopy} {Classes} of {Cycles} and {Singular} {Homology}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {142--146},
     publisher = {mathdoc},
     volume = {246},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2004_246_a8/}
}
TY  - JOUR
AU  - V. V. Dolotin
TI  - Algebraic Structure of the Space of Homotopy Classes of Cycles and Singular Homology
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2004
SP  - 142
EP  - 146
VL  - 246
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2004_246_a8/
LA  - ru
ID  - TM_2004_246_a8
ER  - 
%0 Journal Article
%A V. V. Dolotin
%T Algebraic Structure of the Space of Homotopy Classes of Cycles and Singular Homology
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2004
%P 142-146
%V 246
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2004_246_a8/
%G ru
%F TM_2004_246_a8
V. V. Dolotin. Algebraic Structure of the Space of Homotopy Classes of Cycles and Singular Homology. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 142-146. http://geodesic.mathdoc.fr/item/TM_2004_246_a8/

[1] Dolotin V., “Groups of flagged homotopies and higher gauge theory”, J. Dyn. and Contr. Syst., 5:4 (1999), 547–563 | DOI | MR | Zbl