The Dold-Kan theorem for paracyclic modules
Algebraic Topology
2026-02-10 v1
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.
Cite
@article{arxiv.2602.08158,
title = {The Dold-Kan theorem for paracyclic modules},
author = {Ezra Getzler},
journal= {arXiv preprint arXiv:2602.08158},
year = {2026}
}
Comments
12 pages