Shortening binary complexes and commutativity of K-theory with infinite products
Shortening binary complexes and commutativity of K-theory with infinite products
We show that in Grayson’s model of higher algebraic K-theory using binary acyclic complexes, the complexes of length two suffice to generate the whole group. Moreover, we prove that the comparison map from Nenashev’s model for K 1 K_1 to Grayson’s model for K 1 K_1 is an isomorphism. It follows that algebraic K K -theory of exact categories commutes with infinite products.
1-23
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Winges, Christoph
347e42cd-fbb9-4dfc-80e3-84c79eb5696a
25 March 2020
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Winges, Christoph
347e42cd-fbb9-4dfc-80e3-84c79eb5696a
Kasprowski, Daniel and Winges, Christoph
(2020)
Shortening binary complexes and commutativity of K-theory with infinite products.
Transactions of the American Mathematical Society, Series B, 7 (1), .
(doi:10.1090/btran/43).
Abstract
We show that in Grayson’s model of higher algebraic K-theory using binary acyclic complexes, the complexes of length two suffice to generate the whole group. Moreover, we prove that the comparison map from Nenashev’s model for K 1 K_1 to Grayson’s model for K 1 K_1 is an isomorphism. It follows that algebraic K K -theory of exact categories commutes with infinite products.
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Accepted/In Press date: 31 May 2019
Published date: 25 March 2020
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Local EPrints ID: 478546
URI: http://eprints.soton.ac.uk/id/eprint/478546
PURE UUID: db9ee2a7-55b5-47a7-9fce-f2a98799358f
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Date deposited: 04 Jul 2023 17:48
Last modified: 17 Mar 2024 04:19
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Author:
Daniel Kasprowski
Author:
Christoph Winges
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