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arXiv · 2605.28461

On presentations of K-groups by generators and relations

Bernhard Köck
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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.

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Bernhard Köck. 2026-05-27. On presentations of K-groups by generators and relations. https://arxiv.org/abs/2605.28461

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