Abstract
The inverse involution on a Lie group $G$ is the periodic $2$ transformation $\gamma $ that sends each element $g\in G$ to its inverse $g^{-1}$. The variety of the fixed point set ${\rm Fix}(\gamma )$ is of importance for the relevances with Morse function on the Lie group $G$, and the $G$-representations of the cyclic group $\mathbb{Z}_{2}$. In this paper we develop an approach to calculate the diffeomorphism types of the fixed point sets ${\rm Fix}(\gamma)$ for the simple Lie groups.
Citation
Haibao Duan. Shali Liu. "The fixed point set of the inverse involution on a Lie group." Topol. Methods Nonlinear Anal. 61 (1) 21 - 36, 2023. https://doi.org/10.12775/TMNA.2022.012