Journal of Lie Theory

no. 2
The First and Second Homotopy Groups of a Homogeneous Space of a Complex Linear Algebraic Group
Journal of Lie Theory, Volume 33 (2023) no. 2, pp. 687-700
\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 $\pi_2^\top(X(\CC),x)$.
DOI: 10.5802/jolt.1299
Classification: 14F35, 14M17, 20G20
Keywords: Fundamental group, second homotopy group, homogeneous space, linear algebraic group 
@article{JOLT_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--700},
     year = {2023},
     volume = {33},
     number = {2},
     doi = {10.5802/jolt.1299},
     zbl = {1521.14044},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1299/}
}
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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, Volume 33 (2023) no. 2, pp. 687-700. doi: 10.5802/jolt.1299

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