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Mathematics of the USSR-Izvestiya, 1974, Volume 8, Issue 6, Pages 1271–1285
DOI: https://doi.org/10.1070/IM1974v008n06ABEH002147
(Mi im2010)
 

This article is cited in 20 scientific papers (total in 20 papers)

Formal groups and the Atiyah–Hirzebruch formula

I. M. Krichever
References:
Abstract: In this article, manifolds with actions of compact Lie groups are considered. For each rational Hirzebruch genus $h\colon\Omega_*\to Q$, an “equivariant genus” $h^G$, a homomorphism from the bordism ring of $G$-manifolds to the ring $K(BG)\otimes Q$, is constructed. With the aid of the language of formal groups, for some genera it is proved that for a connected compact Lie group $G$, the image of $h^G$ belongs to the subring $Q\subset K(BG)\otimes Q$. As a consequence, extremely simple relations between the values of these genera on bordism classes of $S^1$-manifolds and submanifolds of its fixed points are found. In particular, a new proof of the Atiyah–Hirzebruch formula is obtained.
Received: 11.12.1973
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1974, Volume 38, Issue 6, Pages 1289–1304
Bibliographic databases:
UDC: 513.83
MSC: Primary 57A65, 53C10, 53C15; Secondary 55B20, 57D15, 57D90
Language: English
Original paper language: Russian
Citation: I. M. Krichever, “Formal groups and the Atiyah–Hirzebruch formula”, Izv. Akad. Nauk SSSR Ser. Mat., 38:6 (1974), 1289–1304; Math. USSR-Izv., 8:6 (1974), 1271–1285
Citation in format AMSBIB
\Bibitem{Kri74}
\by I.~M.~Krichever
\paper Formal groups and the Atiyah--Hirzebruch formula
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1974
\vol 38
\issue 6
\pages 1289--1304
\mathnet{http://mi.mathnet.ru/im2010}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=400267}
\zmath{https://zbmath.org/?q=an:0315.57021}
\transl
\jour Math. USSR-Izv.
\yr 1974
\vol 8
\issue 6
\pages 1271--1285
\crossref{https://doi.org/10.1070/IM1974v008n06ABEH002147}
Linking options:
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  • https://doi.org/10.1070/IM1974v008n06ABEH002147
  • https://www.mathnet.ru/eng/im/v38/i6/p1289
  • This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:753
    Russian version PDF:206
    English version PDF:28
    References:66
    First page:4
     
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