English

$K_1$-groups via binary complexes of fixed length

K-Theory and Homology 2020-01-22 v2

Abstract

We modify Grayson's model of K1K_1 of an exact category to give a presentation whose generators are binary acyclic complexes of length at most kk for any given k2k \ge 2. As a corollary, we obtain another, very short proof of the identification of Nenashev's and Grayson's presentations.

Keywords

Cite

@article{arxiv.1811.10954,
  title  = {$K_1$-groups via binary complexes of fixed length},
  author = {Daniel Kasprowski and Bernhard Köck and Christoph Winges},
  journal= {arXiv preprint arXiv:1811.10954},
  year   = {2020}
}

Comments

10 pages, minor changes following a referee report, to appear in HHA

R2 v1 2026-06-23T06:21:57.136Z