Professor Herbert Gangl herbert.gangl@durham.ac.uk
Professor
On the topological computation of K_4 of the Gaussian and Eisenstein integers
Gangl, Herbert; Dutour Sikiriˇc, M; Gunnells, P; Hanke, J; Schuermann, A; Yasaki, D
Authors
M Dutour Sikiriˇc
P Gunnells
J Hanke
A Schuermann
D Yasaki
Abstract
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.
Citation
Gangl, H., Dutour Sikiriˇc, M., Gunnells, P., Hanke, J., Schuermann, A., & Yasaki, D. (2019). On the topological computation of K_4 of the Gaussian and Eisenstein integers. Journal of Homotopy and Related Structures, 14, 281-291. https://doi.org/10.1007/s40062-018-0212-8
Journal Article Type | Article |
---|---|
Acceptance Date | Jul 25, 2018 |
Online Publication Date | Aug 18, 2018 |
Publication Date | Mar 7, 2019 |
Deposit Date | Aug 7, 2018 |
Publicly Available Date | Dec 19, 2019 |
Journal | Journal of homotopy and related structures. |
Print ISSN | 2193-8407 |
Electronic ISSN | 1512-2891 |
Publisher | Springer |
Peer Reviewed | Peer Reviewed |
Volume | 14 |
Pages | 281-291 |
DOI | https://doi.org/10.1007/s40062-018-0212-8 |
Related Public URLs | https://arxiv.org/abs/1411.0584 |
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Copyright 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
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