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Mat. Sb. (N.S.), 1981, Volume 116(158), Number 3(11), Pages 359–369 (Mi msb2473)  

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

Generators of $S^1$-bordism

O. R. Musin


Abstract: In this paper generators are found for the rings $U^{S^1}_*$ (the unitary $S^1$-bordism ring) and $U_*(S^1,\{\mathbf Z_s\})$ (the unitary bordism ring with actions of the group $S^1$ without fixed points). The generators found are $S^1$-manifolds of the form $(S^3)^k\times\mathbf CP^n/(S^1)^k$. By an obvious construction the ring $U^{S^1}_*$ allows one to establish a relation between numerical invariants of manifolds with unitary actions of $S^1$ and the set of fixed points, without using a theorem of the type of an integrality theorem. In particular, we obtain a new proof of the Atiyah–Hirzebruch formula for the generalized Todd genus of $S^1$-manifolds.
Bibliography: 9 titles.

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English version:
Mathematics of the USSR-Sbornik, 1983, 44:3, 325–334

Bibliographic databases:

UDC: 513.836
MSC: Primary 57R85, 57R77; Secondary 55N22, 55N25
Received: 22.09.1980

Citation: O. R. Musin, “Generators of $S^1$-bordism”, Mat. Sb. (N.S.), 116(158):3(11) (1981), 359–369; Math. USSR-Sb., 44:3 (1983), 325–334

Citation in format AMSBIB
\Bibitem{Mus81}
\by O.~R.~Musin
\paper Generators of $S^1$-bordism
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 116(158)
\issue 3(11)
\pages 359--369
\mathnet{http://mi.mathnet.ru/msb2473}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=665688}
\zmath{https://zbmath.org/?q=an:0508.57027|0494.57015}
\transl
\jour Math. USSR-Sb.
\yr 1983
\vol 44
\issue 3
\pages 325--334
\crossref{https://doi.org/10.1070/SM1983v044n03ABEH000970}


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    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. O. R. Musin, “Converse theorem on equivariant genera”, Russian Math. Surveys, 64:4 (2009), 753–755  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Oleg R. Musin, “On rigid Hirzebruch genera”, Mosc. Math. J., 11:1 (2011), 139–147  mathnet  mathscinet
    3. O. R. Musin, “Circle Actions with Two Fixed Points”, Math. Notes, 100:4 (2016), 636–638  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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