Hutchinson, KevinKevinHutchinson2015-05-202015-05-202013 Cambr2013-08Journal of K-Theoryhttp://hdl.handle.net/10197/6580We introduce a refinement of the Bloch-Wigner complex of a field F. This refinement is complex of modules over the multiplicative group of the field. Instead of computing K 2 (F) and K ind 3 (F) - as the classical Bloch-Wigner complex does - it calculates the second and third integral homology of SL2 (F). On passing to F × -coinvariants we recover the classical Bloch-Wigner complex. We include the case of finite fields throughout the articleenThis article has been accepted for publication by Cambridge University Press and is available in the Journal of K-Theory, Vol: 12, Issue: 1 (2013): 15-68Homology of groupsK-theoryGroup HomologyJournal Article121156810.1017/is013003031jkt132222015-04-20https://creativecommons.org/licenses/by-nc-nd/3.0/ie/