English

A Bloch-Wigner complex for SL_2

K-Theory and Homology 2013-01-21 v2

Abstract

We introduce a refinement of the Bloch-Wigner complex of a field F. This is a complex of modules over the multiplicative group of the field. Instead of computing K_2 and indecomposable K_3 - as the classical Bloch-Wigner complex does - it calculates the second and third integral homology of SL_2 of the field. On passing to coinvariants for the action of the multiplicative group we recover the classical Bloch-Wigner complex. The case of finite fields is included throughout the article.

Keywords

Cite

@article{arxiv.1107.0264,
  title  = {A Bloch-Wigner complex for SL_2},
  author = {Kevin Hutchinson},
  journal= {arXiv preprint arXiv:1107.0264},
  year   = {2013}
}

Comments

To appear in Journal of K-Theory

R2 v1 2026-06-21T18:30:41.915Z