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This article is cited in 20 scientific papers (total in 20 papers)
Formal groups and the Atiyah–Hirzebruch formula
I. M. Krichever
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
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
Linking options:
https://www.mathnet.ru/eng/im2010https://doi.org/10.1070/IM1974v008n06ABEH002147 https://www.mathnet.ru/eng/im/v38/i6/p1289
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Abstract page: | 753 | Russian version PDF: | 206 | English version PDF: | 28 | References: | 65 | First page: | 4 |
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