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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Compact Lie group action and equivariant bordism
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by Shabd Sharan Khare PDF
Proc. Amer. Math. Soc. 92 (1984), 297-300 Request permission


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.
  • P. E. Conner and E. E. Floyd, Differentiable periodic maps, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 33, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1964. MR 0176478
  • Gary C. Hamrick and David C. Royster, Flat Riemannian manifolds are boundaries, Invent. Math. 66 (1982), no. 3, 405–413. MR 662600, DOI 10.1007/BF01389221
  • S. S. Khare, $(\mathcal {F},\mathcal {F}’)$-free bordism and stationary points set, Internat. J. Math. Math. Sci. (to appear).
  • S. S. Khare, Stationary points set and $G$-bordism, Indian J. Pure Appl. Math. 14 (1983), no. 1, 1–4. MR 696828
  • S. S. Khare, Finite group action and equivariant bordism, Pacific J. Math. 116 (1985), no. 1, 39–44. MR 769821
  • Czes Kosniowski, Some equivariant bordism theories vanish, Math. Ann. 242 (1979), no. 1, 59–68. MR 537326, DOI 10.1007/BF01420482
  • R. E. Stong, Equivariant bordism and $(Z_{2})^{k}$ actions, Duke Math. J. 37 (1970), 779–785. MR 271966
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 92 (1984), 297-300
  • MSC: Primary 57S15; Secondary 57R85
  • DOI:
  • MathSciNet review: 754725