Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 142-146
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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/
@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},
year = {2004},
volume = {246},
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
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
%U http://geodesic.mathdoc.fr/item/TM_2004_246_a8/
%G ru
%F TM_2004_246_a8
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 $\pi_k(M)$.
