SOME NOTES ON THE ELLIPTICITY OF NILPOTENT SPACES
Let G be a compact connected Lie group, and X be a rational nilpotent G-space with In this paper, we first provide a necessary and sufficient condition for a nilpotent space to be elliptic. We also give a sufficient condition to determine whether X is elliptic under the condition that each path component of the homotopy fixed point set is elliptic. Moreover, we show that there may exist a non-elliptic path component of if X is not elliptic.
rational homotopy, elliptic space, fixed point set, homotopy fixed point set.
Received: June 2, 2022; Accepted: July 15, 2022; Published: July 28, 2022
How to cite this article: Jian Liu, Sang Xie and Xiugui Liu, Some notes on the ellipticity of nilpotent spaces, JP Journal of Geometry and Topology 28 (2022), 1-12. http://dx.doi.org/10.17654/0972415X22006
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