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Proceedings of the American Mathematical Society

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

 

 

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.


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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