RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Sb.: Year: Volume: Issue: Page: Find

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

$k\langle n\rangle$ 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.

Full text: PDF file (600 kB)
References: PDF file   HTML file

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

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} 

• http://mi.mathnet.ru/eng/msb1997
• http://mi.mathnet.ru/eng/msb/v165/i2/p258

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
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
3. Yu. B. Rudyak, “Orientability of bundles: obstruction theory and applications to $K$-theory”, Math. USSR-Sb., 68:2 (1991), 429–451
•  Number of views: This page: 119 Full text: 32 References: 23