Geodesic
$K_1$-groups via binary complexes of fixed length
Homology, homotopy, and applications, Tome 22 (2020) no. 1, pp. 203-213.

Voir la notice de l'article provenant de la source International Press of Boston

We modify Grayson’s model of $K_1$ of an exact category to give a presentation whose generators are binary acyclic complexes of length at most $k$ for any given $k \geqslant 2$. As a corollary, we obtain another, very short proof of the identification of Nenashev’s and Grayson’s presentations.
DOI : 10.4310/HHA.2020.v22.n1.a12
Classification : 19D06, 18E10, 19B99
Keywords: exact category, binary acyclic complex, Nenashev relation 
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Daniel Kasprowski; Bernhard Köck; Christoph Winges. $K_1$-groups via binary complexes of fixed length. Homology, homotopy, and applications, Tome 22 (2020) no. 1, pp. 203-213. doi : 10.4310/HHA.2020.v22.n1.a12. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2020.v22.n1.a12/

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