Journal of Lie Theory 33 (2023), No. 2, 687--700
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
[Abstract-pdf]
\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.
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