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On K4 Of The Gaussian And Eisenstein Integers
Mathieu Dutour Sikirić,Herbert Gangl,Paul E. Gunnells,Jonathan Hanke,Achill Schürmann,Dan Yasaki +5 more
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In this article, the structure of algebraic K-groups K_4 (Z[i]) and K-4(Z[rho]) is investigated, where i := sqrt{-1} and rho := (1+sqrt{ -3})/2.Abstract:
In this paper we investigate the structure of the algebraic K-groups K_4 (Z[i]) and K_4 (Z[rho]), where i := sqrt{-1} and rho := (1+sqrt{-3})/2. We exploit the close connection between homology groups of GL_n(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 GL_n(R) acts. Our main results are (i) K_4 (Z[i]) is a finite abelian 3-group, and (ii) K_4 (Z[rho]) is trivial.read more
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On the cohomology of linear groups over imaginary quadratic fields
Mathieu Dutour Sikirić,Herbert Gangl,Paul E. Gunnells,Jonathan Hanke,Achill Schürmann,Dan Yasaki +5 more
TL;DR: In this paper, the integral cohomology of Γ up to p-power torsion for small primes p was derived for the case N = 3, D = − 3, − 4 when N = 4.
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Cohomology of Groups
TL;DR: In this paper, an advanced textbook introduces students to cohomology theory and no knowledge of homological algebra is assumed beyond what is normally taught in a first course in algebraic topology.
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