Geodesic
The First and Second Homotopy Groups of a Homogeneous Space of a Complex Linear Algebraic Group
Journal of Lie theory, Tome 33 (2023) no. 2, pp. 687-7
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\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 $\pi_2^\top(X(\CC),x)$.
Classification : 14F35, 14M17, 20G20
Mots-clés : Fundamental group, second homotopy group, homogeneous space, linear algebraic group 
@article{JLT_2023_33_2_JLT_2023_33_2_a9,
     author = {M. Borovoi},
     title = {The {First} and {Second} {Homotopy} {Groups} of a {Homogeneous} {Space} of a {Complex} {Linear} {Algebraic} {Group}},
     journal = {Journal of Lie theory},
     pages = {687--7},
     year = {2023},
     volume = {33},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2023_33_2_JLT_2023_33_2_a9/}
}
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M. Borovoi. The First and Second Homotopy Groups of a Homogeneous Space of a Complex Linear Algebraic Group. Journal of Lie theory, Tome 33 (2023) no. 2, pp. 687-7. http://geodesic.mathdoc.fr/item/JLT_2023_33_2_JLT_2023_33_2_a9/