On presentations of K-groups by generators and relations

2026/05/27 by Bernhard Köck · 1 voice
Mathematics · #math.KT

paper · pdf

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 dévissage isomorphism for K₁ and we give an elementary and fairly simple example in the codomain which appears to require a more sophisticated approach.

Citations

• Exterior power operations on higher K-groups via binary complexes

Discussions

• Bernhard K\"ock: On presentations of K-groups by generators and relations https://arxiv.org/abs/2605.28461 https://arxiv.org/pdf/2605.28461 https://arxiv.org/html/2605.28461 [bsky, 0 points, 0 comments]

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