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Mat. Sb., 2003, Volume 194, Number 1, Pages 23–30 (Mi msb704)  

This article is cited in 6 scientific papers (total in 6 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.

DOI: https://doi.org/10.4213/sm704

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English version:
Sbornik: Mathematics, 2003, 194:1, 21–29

Bibliographic databases:

UDC: 515.164
MSC: Primary 13D15, 18F25; Secondary 11E70, 16S34, 57R67, 57N37
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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. P. M. Akhmet'ev, D. Repovš, M. Cencelj, “Some Algebraic Properties of Cerf Diagrams of One-Parameter Function Families”, Funct. Anal. Appl., 39:3 (2005), 165–174  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Yu. V. Muranov, R. Himenez, “Transfer maps for triples of manifolds”, Math. Notes, 79:3 (2006), 387–398  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. A. Cavicchioli, Yu. V. Muranov, F. Spaggiari, F. Hegenbarth, “On Iterated Browder–Livesay Invariants”, Math. Notes, 86:2 (2009), 196–215  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Chen H., Gao Yu., Tang G., “On K-2 of Fp [Cp2 X Cp2]”, Algebr. Colloq., 20:4 (2013), 681–688  crossref  mathscinet  zmath  isi
    5. Gao Yu., Chen H., “on the Explicit Structure of K-2(Fg) For G a Finite Abelian Group and F a Finite Field”, J. Algebra, 423 (2015), 466–475  crossref  mathscinet  zmath  isi
    6. Yang Zh., Tang G., Liu H., J. Pure Appl. Algebr., 221:4 (2017), 773–779  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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