Abstract
The article investigates the category of manifolds acted upon by a Lie group G in such a way that the orbit of every point is equivariantly diffeomorphic to one of a fixed set S of homogeneous spaces of G. The bordism groups (S-equivariant bordism groups) are defined in a natural way. These groups are described in detail in the special cases of the quasicomplex action of the groups U(1) and SU(2) on quasicomplex manifolds.
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S. P. Novikov, “Adams operators and fixed points,” Izv. Akad. Nauk SSSR, Ser. Matem.,32, No. 6, 1245–1263 (1968).
P. E. Conner and E. E. Floyd, Differentiable Periodic Maps, Academic, New York (1964).
P. E. Conner and E. E. Floyd, “Periodic maps which preserve a complex structure,” Bull. Amer. Math. Soc.,70, No. 4, 574–579 (1964).
W. Y. Hsiang, “A survey on regularity theorems in differentiable compact transformation groups,” Proc. Conf. Transformation Groups, New York (1968).
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Translated from Matematicheskie Zametki, Vol. 10, No. 5, pp. 519–526, November, 1971.
In conclusion, the author thanks S. P. Novikov and A. S. Mishchenko for their interest in the study.
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Karminskii, A.M. Equivariant bordisms. Mathematical Notes of the Academy of Sciences of the USSR 10, 735–739 (1971). https://doi.org/10.1007/BF01109034
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DOI: https://doi.org/10.1007/BF01109034