Pregled bibliografske jedinice broj: 1028875
On the topological computation of K4 of the Gaussian and Eisenstein integers
On the topological computation of K4 of the Gaussian and Eisenstein integers // Journal of Homotopy and Related Structures, 14 (2019), 1; 281-291 doi:10.1007/s40062-018-0212-8 (međunarodna recenzija, članak, znanstveni)
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Naslov
On the topological computation of K4 of the Gaussian and Eisenstein integers
Autori
Dutour Sikirić, Mathieu ; Gangl, Herbert ; Gunnells, Paul E. ; Hanke, Jonathan ; Schürmann, Achill ; Yasaki, Dan
Izvornik
Journal of Homotopy and Related Structures (2193-8407) 14
(2019), 1;
281-291
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
Cohomology of arithmetic groups ; Voronoi reduction theory ; Linear groups over imaginary quadratic fields ; K-theory of number rings
Sažetak
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:= \sqrt{; ; -1}; ; and ρ:= (1+\sqrt{; ; -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.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
Citiraj ovu publikaciju:
Časopis indeksira:
- Current Contents Connect (CCC)
- Web of Science Core Collection (WoSCC)
- Science Citation Index Expanded (SCI-EXP)
- SCI-EXP, SSCI i/ili A&HCI
- Scopus
