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arXiv · 1811.10954

$K_1$-groups via binary complexes of fixed length

Daniel Kasprowski·Bernhard Köck·Christoph Winges
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Abstract

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 $k \ge 2$. As a corollary, we obtain another, very short proof of the identification of Nenashev's and Grayson's presentations.

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Daniel Kasprowski, Bernhard Köck, Christoph Winges. 2018-11-27. $K_1$-groups via binary complexes of fixed length. https://doi.org/10.4310/hha.2020.v22.n1.a12

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