The Hurewicz theorem for cubical homology

The Hurewicz theorem for cubical homology

We give an elementary proof of the Hurewicz theorem relating homotopy and homology groups of a cubical Kan complex. Our approach is based on the notion of a loop space of a cubical set, developed in a companion paper “Homotopy groups of cubical sets” by the first two authors.

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Veröffentlicht in:Mathematische Zeitschrift 2023-12, Vol.305 (4), Article 61
Hauptverfasser: Carranza, Daniel, Kapulkin, Krzysztof, Tonks, Andrew
Format: Artikel
Sprache:eng
Schlagworte:
Homology
Mathematics
Mathematics and Statistics
Theorems
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Beschreibung
Zusammenfassung:We give an elementary proof of the Hurewicz theorem relating homotopy and homology groups of a cubical Kan complex. Our approach is based on the notion of a loop space of a cubical set, developed in a companion paper “Homotopy groups of cubical sets” by the first two authors.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-023-03352-0