K1-groups via binary complexes of fixed length
K1-groups via binary complexes of fixed length
We modify Grayson's model of K1 of an exact category to give a presentation whose generators are binary acyclic complexes of length at most k for any given k ≥ 2. As a corollary, we obtain another, very short proof of the identification of Nenashev's and Grayson's presentations.
Nenashev relation, binary acyclic complex, exact category
203-213
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Koeck, Bernhard
84d11519-7828-43a6-852b-0c1b80edeef9
Winges, Christoph
347e42cd-fbb9-4dfc-80e3-84c79eb5696a
2020
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Koeck, Bernhard
84d11519-7828-43a6-852b-0c1b80edeef9
Winges, Christoph
347e42cd-fbb9-4dfc-80e3-84c79eb5696a
Kasprowski, Daniel, Koeck, Bernhard and Winges, Christoph
(2020)
K1-groups via binary complexes of fixed length.
Homology, Homotopy and Applications, 22 (1), .
(doi:10.4310/HHA.2020.v22.n1.a12).
Abstract
We modify Grayson's model of K1 of an exact category to give a presentation whose generators are binary acyclic complexes of length at most k for any given k ≥ 2. As a corollary, we obtain another, very short proof of the identification of Nenashev's and Grayson's presentations.
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Accepted/In Press date: 8 July 2019
e-pub ahead of print date: 20 November 2019
Published date: 2020
Additional Information:
Funding Information:
Winges acknowledges support by the Max Planck Society and Wolfgang Lück’s ERC Advanced Grant “KL2MG-interactions” (no. 662400). Kasprowski and Winges were funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – GZ 2047/1, Project-ID 390685813. Received May 15, 2019, revised June 12, 2019, July 4, 2019; published on November 20, 2019. 2010 Mathematics Subject Classification: Primary 19D06; Secondary 18E10, 19B99. Key words and phrases: exact category, binary acyclic complex, Nenashev relation. Article available at http://dx.doi.org/10.4310/HHA.2020.v22.n1.a12 Copyright ©c 2019, Daniel Kasprowski, Bernhard Köck and Christoph Winges. Permission to copy for private use granted.
Publisher Copyright:
© 2020, International Press.
Keywords:
Nenashev relation, binary acyclic complex, exact category
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Local EPrints ID: 426690
URI: http://eprints.soton.ac.uk/id/eprint/426690
PURE UUID: a21a4b55-1789-42f1-b8fd-5b69e7f7e187
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Date deposited: 10 Dec 2018 17:31
Last modified: 16 Mar 2024 04:51
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Author:
Daniel Kasprowski
Author:
Christoph Winges
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