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Finding the fundamental2nd homotopy group $\pi_2(G^\mathbb{C}/P)$

Let $G$ be a compact connected and simply connected Lie group and $G^\mathbb{C}$ be the complexification of Lie group (with is diffeomorphic with $G^\mathbb{C}\cong T^*G$) then I am looking for finding the fundamental2nd homotopy group   $\pi_2(G^\mathbb{C}/P)$ where $P$ here is Parabolic subgroup. Is there any method or referrence ?

Finding the fundamental group $\pi_2(G^\mathbb{C}/P)$

Let $G$ be a compact connected and simply connected Lie group and $G^\mathbb{C}$ be the complexification of Lie group (with is diffeomorphic with $G^\mathbb{C}\cong T^*G$) then I am looking for finding the fundamental group $\pi_2(G^\mathbb{C}/P)$ where $P$ here is Parabolic subgroup. Is there any method or referrence ?

Finding the 2nd homotopy group $\pi_2(G^\mathbb{C}/P)$

Let $G$ be a compact connected and simply connected Lie group and $G^\mathbb{C}$ be the complexification of Lie group (with is diffeomorphic with $G^\mathbb{C}\cong T^*G$) then I am looking for finding the 2nd homotopy group   $\pi_2(G^\mathbb{C}/P)$ where $P$ here is Parabolic subgroup. Is there any method or referrence ?

Source Link
user21574
user21574

Finding the fundamental group $\pi_2(G^\mathbb{C}/P)$

Let $G$ be a compact connected and simply connected Lie group and $G^\mathbb{C}$ be the complexification of Lie group (with is diffeomorphic with $G^\mathbb{C}\cong T^*G$) then I am looking for finding the fundamental group $\pi_2(G^\mathbb{C}/P)$ where $P$ here is Parabolic subgroup. Is there any method or referrence ?