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

2003/01/06 by Valery Dolotin, Valery Valerievich Dolotin, Dolotin, Valery
Mathematics · #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.AT #math.KT

paper · pdf · doi:10.48550/arxiv.math/0301043

6 pages LaTeX, 5 figures

arxiv created 2003/01/06 · openalex publication_date 2003/01/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 π_k(M).

Related

• Homology of spaces of regular loops in the sphere
• Diagrams of classifying spaces and k-fold Boolean algebras
• The homotopy groups of a homotopy group completion
• Loop spaces and homotopy operations
• Natural transformations relating homotopy and singular homology functors