On presentations of K-groups by generators and relations
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913168207380480 |
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| author | Köck, Bernhard |
| author_facet | Köck, Bernhard |
| contents | In Grayson's combinatorial description of higher K-groups, the generators are bounded acyclic binary multi-complexes of arbitrary size. Generalising work by Kasprowski, Winges and the author, we show in this paper that multi-complexes of bounded size suffice and we provide the corresponding relations. Furthermore, we report on the progress in our attempt to algebraically prove the surjectivity of Quillen's dévissage isomorphism for K_1 and we give an elementary and fairly simple example in the codomain which appears to require a more sophisticated approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28461 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On presentations of K-groups by generators and relations Köck, Bernhard K-Theory and Homology 19D99 (Primary), 19B99 (Secondary) In Grayson's combinatorial description of higher K-groups, the generators are bounded acyclic binary multi-complexes of arbitrary size. Generalising work by Kasprowski, Winges and the author, we show in this paper that multi-complexes of bounded size suffice and we provide the corresponding relations. Furthermore, we report on the progress in our attempt to algebraically prove the surjectivity of Quillen's dévissage isomorphism for K_1 and we give an elementary and fairly simple example in the codomain which appears to require a more sophisticated approach. |
| title | On presentations of K-groups by generators and relations |
| topic | K-Theory and Homology 19D99 (Primary), 19B99 (Secondary) |
| url | https://arxiv.org/abs/2605.28461 |