Free actions and complex cobordism
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- by Connor Lazarov and Arthur G. Wasserman PDF
- Proc. Amer. Math. Soc. 47 (1975), 215-217 Request permission
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
- Robert E. Stong, Notes on cobordism theory, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. Mathematical notes. MR 0248858
- Connor Lazarov and Arthur Wasserman, Complex actions of Lie groups, Memoirs of the American Mathematical Society, No. 137, American Mathematical Society, Providence, R.I., 1973. MR 0339233
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 47 (1975), 215-217
- DOI: https://doi.org/10.1090/S0002-9939-1975-0350759-2
- MathSciNet review: 0350759