
Journal of Lie Theory 33 (2023), No. 2, 687700 Copyright Heldermann Verlag 2023 The First and Second Homotopy Groups of a Homogeneous Space of a Complex Linear Algebraic Group Mikhail Borovoi Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Israel borovoi@tauex.tau.ac.il [Abstractpdf] \newcommand{\CC}{{\mathbb{C}}} \def\top{{\textup{top}}} Let $X$ be a homogeneous space of a connected linear algebraic group $G$ defined over the field of complex numbers $\CC$. Let $x\in X(\CC)$ be a point. We denote by $H$ the stabilizer of $x$ in $G$. When $H$ is connected, we compute the topological fundamental group $\pi_1^\top(X(\CC),x)$. Moreover, we compute the second homotopy group $\pi_2^\top(X(\CC),x)$. Keywords: Fundamental group, second homotopy group, homogeneous space, linear algebraic group. MSC: 14F35, 14M17, 20G20. [ Fulltextpdf (140 KB)] for subscribers only. 