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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2004, Volume 246, Pages 142–146
(Mi tm150)
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Algebraic Structure of the Space of Homotopy Classes of Cycles and Singular Homology
V. V. Dolotin Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
Abstract:
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 $\pi_k(M)$.
Received in February 2004
Citation:
V. V. Dolotin, “Algebraic Structure of the Space of Homotopy Classes of Cycles and Singular Homology”, Algebraic geometry: Methods, relations, and applications, Collected papers. Dedicated to the memory of Andrei Nikolaevich Tyurin, corresponding member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 246, Nauka, MAIK «Nauka/Inteperiodika», M., 2004, 142–146; Proc. Steklov Inst. Math., 246 (2004), 129–133
Linking options:
https://www.mathnet.ru/eng/tm150 https://www.mathnet.ru/eng/tm/v246/p142
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