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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Oriented and weakly complex bordism algebra of free periodic maps


Author: Katsuyuki Shibata
Journal: Trans. Amer. Math. Soc. 177 (1973), 199-220
MSC: Primary 57D85
DOI: https://doi.org/10.1090/S0002-9947-1973-0315734-5
MathSciNet review: 0315734
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Abstract: Free cyclic actions on a closed oriented (weakly almost complex, respectively) manifold which preserve the orientation (weakly complex structure) are considered from the viewpoint of equivariant bordism theory. The author gives an explicit presentation of the oriented bordism module structure and multiplicative structure of all orientation preserving (and reversing) free involutions. The odd period and weakly complex cases are also determined with the aid of the notion of formal group laws. These results are applied to a nonexistence problem for certain equivariant maps.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0315734-5
Keywords: Oriented bordism, weakly complex bordism, free periodic maps, equivariant bordism theory, free differentiable involutions, equivariant maps, Pontrjagin product, Smith homomorphism, cobordism characteristic classes, formal group law, logarithm of a formal group, Miščenko series
Article copyright: © Copyright 1973 American Mathematical Society