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This article is cited in 7 scientific papers (total in 7 papers)
$K_2$ for the simplest integral group rings and topological applications
P. M. Akhmet'ev Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation
Abstract:
We calculate the group $K_2(\Lambda)$, where
$\Lambda=\mathbb Z/2[\pi]$ is the group ring of a fundamental group with coefficients in the field $\mathbb Z/2$ and $\pi=\mathbb Z/2\oplus\mathbb Z/2$ is the simplest elementary Abelian group of rank $2$. Using these calculations we estimate from below the value $K_2(\overline\Lambda)$, where $\overline\Lambda$ is the integral group ring of the group $\pi$. This calculation yields certain corollaries in the theory of pseudo-isotopies, since the group
$Wh_2(\mathbb Z/2^2)$ turns out to be non-trivial. Constructions in differential topology are discussed that lead to calculations of $Wh_2$-valued invariants.
Received: 13.05.2002
Citation:
P. M. Akhmet'ev, “$K_2$ for the simplest integral group rings and topological applications”, Mat. Sb., 194:1 (2003), 23–30; Sb. Math., 194:1 (2003), 21–29
Linking options:
https://www.mathnet.ru/eng/sm704https://doi.org/10.1070/SM2003v194n01ABEH000704 https://www.mathnet.ru/eng/sm/v194/i1/p23
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Abstract page: | 445 | Russian version PDF: | 238 | English version PDF: | 26 | References: | 65 | First page: | 1 |
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