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

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

2003-01-06

arxiv.org/abs/math/0301043v1

Mathematics

Algebraic Topology

6 pages LaTeX, 5 figures

Scientific paper

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 $\pi_k(M)$.

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