English

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

R2 v1 2026-07-01T10:27:05.489Z