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