Geodesic
Obstructions to the existence of $S^1$-actions. Bordism of ramified coverings
Izvestiya. Mathematics, Tome 10 (1976) no. 4, pp. 783-797 
I. M. Krichever. Obstructions to the existence of $S^1$-actions. Bordism of ramified coverings. Izvestiya. Mathematics, Tome 10 (1976) no. 4, pp. 783-797. http://geodesic.mathdoc.fr/item/IM2_1976_10_4_a6/
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     title = {Obstructions to the existence of $S^1$-actions. {Bordism} of ramified coverings},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this article the author proves that the values of the multiplicative genera $A_k$ under discussion, where $k=2,3,\dots$, are obstructions to the existence of nontrivial $S^1$-actions on a unitary manifold whose first Chern class is divisible by $k$. The effective computation of these obstructions is carried out for algebraic manifolds. Simultaneously, formulas for the bordism class of a ramified covering are obtained. Bibliography: 8 titles.

[1] Krichever I. M., “Formalnye gruppy i formula Ati–Khirtsebrukha”, Izv. AN SSSR. Ser. matem., 38 (1974), 1289–1304 | MR | Zbl

[2] Bukhshtaber V. M., “Kharakter Chzhenya–Dolda v teorii kobordizmov. I”, Matem. sb., 83(125) (1970), 575–595 | Zbl

[3] Hirzebruch F., The signature of ramified coverings, Global Analysis papers on honour of Kodairu, Tokyo, 1969 | MR

[4] Palais R., Theory of $G$-spaces, Memoirs A. M. S., 1960 | Zbl

[5] Dold A., “Relations between ordinary and extraordinary cohomology”, Colloquium on Algebraic Topology, Aarhus, 1962

[6] Novikov S. P., “Operatory Adamsa i nepodvizhnye tochki”, Izv. AN SSSR. Ser. matem., 32 (1968), 1245–1263 | MR

[7] Stewart T., “Lifting group actions in fibre bundles”, Ann. Math., 74 (1961), 192–198 | DOI | MR | Zbl

[8] Atiyah M., Hirzebruch F., “Spin-manifolds and group actions”, Essay Topol. and Relat. Topics, Berlin, 1970, 28–38 | MR