On presentations of K-groups by generators and relations
K-Theory and Homology
2026-05-28 v1
Abstract
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 d\'evissage isomorphism for K_1 and we give an elementary and fairly simple example in the codomain which appears to require a more sophisticated approach.
Cite
@article{arxiv.2605.28461,
title = {On presentations of K-groups by generators and relations},
author = {Bernhard Köck},
journal= {arXiv preprint arXiv:2605.28461},
year = {2026}
}
Comments
13 pages; to appear in a conference volume published by Springer in the series: Proceedings in Mathematics and Statistics