The Dold-Kan theorem for paracyclic modules
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914314877665280 |
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| author | Getzler, Ezra |
| author_facet | Getzler, Ezra |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08158 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Dold-Kan theorem for paracyclic modules Getzler, Ezra Algebraic Topology 18G31 (Primary) 16E40 (Secondary) 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. |
| title | The Dold-Kan theorem for paracyclic modules |
| topic | Algebraic Topology 18G31 (Primary) 16E40 (Secondary) |
| url | https://arxiv.org/abs/2602.08158 |