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A Bloch-Wigner complex for SL2

Published online by Cambridge University Press:  22 April 2013

Kevin Hutchinson
Kevin Hutchinson*
Affiliation:
School of Mathematical Sciences, University College DublinIrelandkevin.hutchinson@ucd.ie
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Abstract

We 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 K2(F) and Kind3(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 article.

Keywords

K-theoryGroup Homology19G9920G10

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Type
Research Article
Information
Journal of K-Theory , Volume 12 , Issue 1: Nanjing Special Issue on K-theory, number theory and geometry , August 2013 , pp. 15 - 68
Copyright
Copyright © ISOPP 2013 

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