On presentations of K-groups by generators and relations
On presentations of K-groups by generators and relations
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 devissage isomorphism for K_1 and we give an elementary and fairly simple example in the codomain which appears to require a more sophisticated approach.
binary multi complexes of bounded size, ladder relation, Quillen’s Devissage Theorem
Koeck, Bernhard
84d11519-7828-43a6-852b-0c1b80edeef9
Koeck, Bernhard
84d11519-7828-43a6-852b-0c1b80edeef9
Koeck, Bernhard
(2026)
On presentations of K-groups by generators and relations.
In Proceedings of Arithmetic, K-Theory and Algebraic Cycles - international conference and workshop: Ohio State University, Columbus, Ohio, USA, May 27-31, 2025.
13 pp
.
(In Press)
Record type:
Conference or Workshop Item
(Paper)
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 devissage isomorphism for K_1 and we give an elementary and fairly simple example in the codomain which appears to require a more sophisticated approach.
Text
devissage4
- Author's Original
More information
Accepted/In Press date: 23 April 2026
Venue - Dates:
Arithmetic, K-Theory and Algebraic Cycles, Ohio State University, Columbus, United States, 2025-05-27 - 2025-05-31
Keywords:
binary multi complexes of bounded size, ladder relation, Quillen’s Devissage Theorem
Identifiers
Local EPrints ID: 512657
URI: http://eprints.soton.ac.uk/id/eprint/512657
PURE UUID: eebca518-1ad2-4c5b-abe7-deafb1e1a48f
Catalogue record
Date deposited: 14 Jul 2026 16:48
Last modified: 30 Jul 2026 01:39
Export record
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
