The fixed point set of the inverse involution on a Lie group - Duan, Haibao; Liu, Shali (Topological Methods in Nonlinear Analysis, 2023)
The inverse involution on a Lie group $G$ is the periodic $2$ transformation$γ $ that sends each element $g\in G$ to its inverse $g^{-1}$. Thevariety of the fixed point set $\Fix(γ )$ is of importance for therelevances with Morse function on the Lie group $G$, and the $G$-representationsof the cyclic group $\mathbb{Z}_{2}$. In this paper we develop an approach to calculate the diffeomorphism types of the fixed point sets $\Fix(γ)$ for the simple Lie groups.