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Compact Lie group action and equivariant bordism


Author: Shabd Sharan Khare
Journal: Proc. Amer. Math. Soc. 92 (1984), 297-300
MSC: Primary 57S15; Secondary 57R85
DOI: https://doi.org/10.1090/S0002-9939-1984-0754725-X
MathSciNet review: 754725
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Abstract: Let $ G$ be a compact Lie group and $ H$ a compact Lie subgroup of $ G$ contained in the center of $ G$ with $ {H^m}$ the maximal subgroup in the center, $ H$ being $ H$-boundary. Let $ pr:{H^m} \to H$ be the projection onto the $ r$th factor and $ {H_r}$ be the $ r$th factor of $ {H^m}$. Let $ \{ {L_r}\} $ be a family of subgroups of $ G$ such that $ {L_r} \cap {H_r}$ is nontrivial. Consider a $ G$-manifold $ {M^n}$ with $ pr({G_x} \cap {H^m})$ trivial or containing $ {L_r}$, for every $ x$ in $ {M^n}$. The main result of the paper is that if $ \forall x \in {M^n}$, $ {p_r}({G_x} \cap {H^m})$ is trivial at least for one $ r$, then $ {M^n}$ is a $ G$-boundary.


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

  • [1] P. E. Conner and E. E. Floyd, Differentiable periodic maps, Springer-Verlag, Berlin, 1964. MR 0176478 (31:750)
  • [2] G. C. Hamrick and D. C. Royster, Flat Riemannian manifolds are boundaries, Invent. Math 66 (1982). MR 662600 (83h:53051)
  • [3] S. S. Khare, $ (\mathcal{F},\mathcal{F}')$-free bordism and stationary points set, Internat. J. Math. Math. Sci. (to appear).
  • [4] -, Stationary points set and $ G$-bordism, Indian J. Pure Appl. Math. 14 (1983), 1-4. MR 696828 (84k:57023)
  • [5] -, Finite group action and equivariant bordism Pacific J. Math. (to appear). MR 769821 (86e:57034)
  • [6] C. Kosniowski, Some equivariant bordism theories vanish, Math. Ann. 242 (1979). MR 537326 (80e:57041)
  • [7] R. E. Stong, Equivariant bordism and $ {({{\mathbf{Z}}_2})^k}$-actions, Duke Math. J. 37 (1970). MR 0271966 (42:6847)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0754725-X
Keywords: $ H$-boundary, admissible pair, $ \{ {L_r}\} $-type action, pseudo stationary point, equivariant bordism
Article copyright: © Copyright 1984 American Mathematical Society

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