Gangl, Herbert and Dutour Sikiriˇc, M and Gunnells, P and Hanke, J and Schuermann, A and Yasaki, D (2019) 'On the topological computation of K_4 of the Gaussian and Eisenstein integers.', Journal of homotopy and related structures., 14 . pp. 281-291.
In this paper we use topological tools to investigate the structure of the algebraic K-groups K4(R) for R=Z[i] and R=Z[ρ] where i:=−1−−−√ and ρ:=(1+−3−−−√)/2. We exploit the close connection between homology groups of GLn(R) for n≤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 result is that K4(Z[i]) and K4(Z[ρ]) have no p-torsion for p≥5.
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||https://doi.org/10.1007/s40062-018-0212-8|
|Publisher statement:||This is a post-peer-review, pre-copyedit version of an article published in Journal of homotopy and related structures. The final authenticated version is available online at: https://doi.org/10.1007/s40062-018-0212-8|
|Date accepted:||25 July 2018|
|Date deposited:||19 December 2019|
|Date of first online publication:||18 August 2018|
|Date first made open access:||19 December 2019|
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