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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Free actions and complex cobordism


Authors: Connor Lazarov and Arthur G. Wasserman
Journal: Proc. Amer. Math. Soc. 47 (1975), 215-217
DOI: https://doi.org/10.1090/S0002-9939-1975-0350759-2
MathSciNet review: 0350759
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Abstract | References | Additional Information

Abstract: Connor and Floyd have observed that a free action of a finite group $ G$ on a compact manifold $ M$ preserving a stable almost complex structure produces a stably almost complex quotient manifold $ M/G$. Hence, the bordism group of such actions, $ U_ \ast ^{G,{\text{free}}}$, is just $ {U_ \ast }(BG)$. If $ G$ is not finite or abelian, but an arbitrary compact Lie group, the tangent bundle along the fibres gives trouble. Nevertheless, it is shown that if $ {H^ \ast }(BG)$ is torsion free then $ U_ \ast ^{G,{\text{free}}} \approx {U_ \ast }(BG)$.


References [Enhancements On Off] (What's this?)

  • [1] Robert E. Stong, Notes on cobordism theory, Mathematical notes, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. MR 0248858
  • [2] Connor Lazarov and Arthur Wasserman, Complex actions of Lie groups, American Mathematical Society, Providence, R.I., 1973. Memoirs of the American Mathematical Society, No. 137. MR 0339233


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0350759-2
Keywords: Free actions, complex bordism
Article copyright: © Copyright 1975 American Mathematical Society