Unpublished Paper
On K4 Of The Gaussian And Eisenstein Integers
(2010)
Abstract
Abstract. In this paper we investigate the structure of the algebraic K-groups K4(Z[i]) and K4(Z[ρ]), where i := √ −1 and ρ := (1 + √ −3)/2. We exploit the close connection between homology groups of GLn(R) for n 6 5 and those of related classifying spaces, then compute the former using Voronoi’s reduction theory of positive definite quadratic and Hermitian forms to produce a very large finite cell complex on which GLn(R) acts. Our main results are (i) K4(Z[i]) is a finite abelian 3-group, and (ii) K4(Z[ρ]) is trivial.
Disciplines
Publication Date
2010
Comments
This is an unpublished paper harvested from arXiv.
Citation Information
Mathieu Dutour Sikiric, Herbert Gangl, Paul Gunnells, Jonathan Hanke, et al.. "On K4 Of The Gaussian And Eisenstein Integers" (2010) Available at: http://works.bepress.com/paul_gunnells/44/