JP Journal of Geometry and Topology

The JP Journal of Geometry and Topology publishes articles in all branches of geometry and topology, with applications to physics. It covers areas such as differential geometry, algebraic topology, and geometric aspects of mathematical physics. Survey articles are also welcome.

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SOME NOTES ON THE ELLIPTICITY OF NILPOTENT SPACES

Authors

  • Jian Liu
  • Sang Xie
  • Xiugui Liu

Keywords:

rational homotopy, elliptic space, fixed point set, homotopy fixed point set.

DOI:

https://doi.org/10.17654/0972415X22006

Abstract

Let $G$ be a compact connected Lie group, and $X$ be a rational nilpotent $G$-space with $\operatorname{dim} \pi_*(X)<\infty$.  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 $X_{\mathbb{Q}}^{h G}$  is elliptic. Moreover, we show that there may exist a non-elliptic path component of $X_{\mathbb{Q}}^{h G}$  if $X$ is not elliptic.

Received: June 2, 2022 
Accepted: July 15, 2022

References

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Published

2022-07-28

Issue

Vol. 28 (2022)

Section

Articles

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How to Cite

SOME NOTES ON THE ELLIPTICITY OF NILPOTENT SPACES. (2022). JP Journal of Geometry and Topology, 28, 1-12. https://doi.org/10.17654/0972415X22006

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