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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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Keywords: <IMG WIDTH="24" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$H$">-boundary, admissible pair, <!– MATH $\{ {L_r}\}$ –> <IMG WIDTH="48" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$\{ {L_r}\}$">-type action, pseudo stationary point, equivariant bordism
Article copyright: © Copyright 1984 American Mathematical Society