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Sbornik: Mathematics, 2003, Volume 194, Issue 1, Pages 21–29
DOI: https://doi.org/10.1070/SM2003v194n01ABEH000704
(Mi sm704)
 

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
References:
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
Russian version:
Matematicheskii Sbornik, 2003, Volume 194, Number 1, Pages 23–30
DOI: https://doi.org/10.4213/sm704
Bibliographic databases:
UDC: 515.164
MSC: Primary 13D15, 18F25; Secondary 11E70, 16S34, 57R67, 57N37
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/sm704
  • https://doi.org/10.1070/SM2003v194n01ABEH000704
  • https://www.mathnet.ru/eng/sm/v194/i1/p23
  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
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    Abstract page:445
    Russian version PDF:238
    English version PDF:26
    References:65
    First page:1
     
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