论文标题
复杂线性代数组的同一空间的第一和第二均匀群组
The first and second homotopy groups of a homogeneous space of a complex linear algebraic group
论文作者
论文摘要
令$ x $为在复数$ \ mathbb c $的字段中定义的连接线性代数$ g $的均匀空间。令$ x \ in x（{\ mathbb c}）$是一个点。我们用$ h $表示$ x $ in $ g $的稳定器。当连接$ H $时，我们计算拓扑基本组$π_1^{\ rm top}（x（{\ Mathbb c}），x）$。此外，我们计算第二个同型组$π_2^{\ rm top}（x（{\ mathbb c}），x）$。
Let $X$ be a homogeneous space of a connected linear algebraic group $G$ defined over the field of complex numbers $\mathbb C$. Let $x\in X({\mathbb C})$ be a point. We denote by $H$ the stabilizer of $x$ in $G$. When $H$ is connected, we compute the topological fundamental group $π_1^{\rm top}(X({\mathbb C}),x)$. Moreover, we compute the second homotopy group $π_2^{\rm top}(X({\mathbb C}),x)$.
