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Mat. Sb. (N.S.), 1984, Volume 123(165), Number 2, Pages 258–268 (Mi msb1997)  

This article is cited in 3 scientific papers (total in 3 papers)

$k\langle n\rangle$ bordism theories with singularities and $k\langle n\rangle$-orientability of bundles

A. V. Khokhlov


Abstract: This paper gives a description of the homotopy types of the spectra $k\langle n\rangle$ which represent bordism theories with singularities, and for which $\pi_*(k\langle n\rangle)=Z_{(p)}[t]$, $\dim t=2p^n-2$. The invariants of the Postnikov tower of the spectrum $k\langle n\rangle$ are higher operations $\widetilde Q_n^{(s)}$ where $\widetilde Q_n^{(0)}\in HZ_{(p)}*(HZ_{(p)})$ and the element $\widetilde Q_n^{(s+1)}$ is constructed from the relation $\widetilde Q_n^{(0)}\widetilde Q_n^{(s)}=0$. The order of the higher operation, i.e. the order of the corresponding element $\alpha_s$ in the cohomology of the stage $k^{s-1}\langle n\rangle$, is equal to $p^s$. Moreover, the question of the action of the higher operations $\widetilde Q_n^{(s)}$ on Thom classes of vector bundles and sphere bundles is solved, which gives a necessary and sufficient condition for orientability of vector bundles and sphere bundles in $k\langle n\rangle$-theory.
Bibliography: 10 titles.

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English version:
Mathematics of the USSR-Sbornik, 1985, 51:1, 255–266

Bibliographic databases:

UDC: 515.142.425
MSC: Primary 55N20, 55N22; Secondary 55P42, 55R25
Received: 22.02.1983

Citation: A. V. Khokhlov, “$k\langle n\rangle$ bordism theories with singularities and $k\langle n\rangle$-orientability of bundles”, Mat. Sb. (N.S.), 123(165):2 (1984), 258–268; Math. USSR-Sb., 51:1 (1985), 255–266

Citation in format AMSBIB
\Bibitem{Kho84}
\by A.~V.~Khokhlov
\paper $k\langle n\rangle$ bordism theories with singularities and $k\langle n\rangle$-orientability of bundles
\jour Mat. Sb. (N.S.)
\yr 1984
\vol 123(165)
\issue 2
\pages 258--268
\mathnet{http://mi.mathnet.ru/msb1997}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=732389}
\zmath{https://zbmath.org/?q=an:0567.55003|0547.55001}
\transl
\jour Math. USSR-Sb.
\yr 1985
\vol 51
\issue 1
\pages 255--266
\crossref{https://doi.org/10.1070/SM1985v051n01ABEH002858}


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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. A. V. Khokhlov, “On the composition of cohomological operations”, Russian Math. Surveys, 41:6 (1986), 209–210  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Rudiak I., “On the Orientability of Spherical Fibrations, Topological and Piecewise-Linear Bundles with Respect to the Complex K-Theory”, 298, no. 6, 1988, 1338–1341  isi
    3. Yu. B. Rudyak, “Orientability of bundles: obstruction theory and applications to $K$-theory”, Math. USSR-Sb., 68:2 (1991), 429–451  mathnet  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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