On the bordism of almost free actions
Author:
R. Paul Beem
Journal:
Trans. Amer. Math. Soc. 225 (1977), 83105
MSC:
Primary 57D85
MathSciNet review:
0425991
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Abstract: An ``almost free'' action on a manifold is one in which only the included may possibly fix points of the manifold. For k = 2, these are the stationarypoint free actions. It is shown that almost free bordism is generated by three subalgebras: the extension from actions, a coset of extensions being the restrictions of circle actions and a certain ideal of elements which annihilate the whole ring. The additive structure is determined. Free bordism is shown to split as an algebra. It is shown that the kernel of the extension homomorphism from to bordism is equal to the image of the corresponding restriction homomorphism.
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 P. E. Conner and E. E. Floyd, Differentiate periodic maps, Ergebnisse Math. Grenzgebiete, N. F., Band 33, SpringerVerlag, Berlin; Academic Press, New York, 1964. MR 31 #750.
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 Yutaka Katsube, Principal oriented bordism algebra , Hiroshima Math. J. 4 (1974), 265277. MR 50 # 1270. MR 0348775 (50:1270)
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 C. N. Lee, Equivariant homology theories, Proc. Conf. on Transformation Groups (New Orleans, La., 1967), SpringerVerlag, Berlin and New York, 1968, pp. 237244. MR 40 #3538. MR 0250299 (40:3538)
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 R. J. Rowlett, Bounding a free action of an abelian group, Duke Math. J. 41 (1974), 381385. MR 49 #6257. MR 0341506 (49:6257)
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 R. E. Stong, Equivariant bordism and Smith theory. IV, Trans. Amer. Math. Soc. 215 (1976), 313321. MR 0405464 (53:9257)
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 , On the bordism algebra of involutions, Unpublished notes, University of Virginia.
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 , Unoriented bordism and actions of finite groups, Mem. Amer. Math. Soc. No. 103 (1970). MR 42 #8522. MR 0273645 (42:8522)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197704259916
PII:
S 00029947(1977)04259916
Keywords:
Equivariant bordism
Article copyright:
© Copyright 1977 American Mathematical Society
