The Dold-Kan theorem for paracyclic modules

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Ezra Getzler
DOI: 10.48550/arxiv.2602.08158
Cited by: 0

Abstract

We study the Karoubi operator on the unnormalized chain complex of a paracyclic module; its restriction to the normalized chain complex has previously been considered by Dwyer and Kan, and in the cyclic case by Cuntz and Quillen. We obtain a direct proof of the Dold-Kan theorem for paracyclic modules of Dwyer and Kan, by directly relating the Karoubi operator to projection to the normalized subcomplex.

Fields of Study & Subjects

Homotopy and Cohomology in Algebraic Topology Algebraic structures and combinatorial models Advanced Combinatorial Mathematics

Publication details

Journal / source
arXiv (Cornell University)
Publication date
8 February 2026
Language
EN
Document type
Preprint