principal bundle of homogeneous spaces where the group is a product

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Let $G$ be a connected topological group. Let $A,B$ be two closed normal subgroups such that $A$ is central. Suppose $Acap B=e$ and $G=Atimes B$ . Let $H$ be a closed subgroup. Consider the principal fiber bundle $pi: G/Hrightarrow G/AH$.



  1. Can we reduce the situation to $ A/(Acap H)times B/(Bcap H)rightarrow B/(Bcap AH)$, $Big(a(Acap H),b(Bcap H)Big)mapsto b(Bcap AH) $?


  2. Is this bundle trivial? What are the sections?




algebraic-topology lie-groups topological-groups fiber-bundles




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    Let $G$ be a connected topological group. Let $A,B$ be two closed normal subgroups such that $A$ is central. Suppose $Acap B=e$ and $G=Atimes B$ . Let $H$ be a closed subgroup. Consider the principal fiber bundle $pi: G/Hrightarrow G/AH$.



    1. Can we reduce the situation to $ A/(Acap H)times B/(Bcap H)rightarrow B/(Bcap AH)$, $Big(a(Acap H),b(Bcap H)Big)mapsto b(Bcap AH) $?


    2. Is this bundle trivial? What are the sections?




    algebraic-topology lie-groups topological-groups fiber-bundles




    share|cite|improve this question





















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      Let $G$ be a connected topological group. Let $A,B$ be two closed normal subgroups such that $A$ is central. Suppose $Acap B=e$ and $G=Atimes B$ . Let $H$ be a closed subgroup. Consider the principal fiber bundle $pi: G/Hrightarrow G/AH$.



      1. Can we reduce the situation to $ A/(Acap H)times B/(Bcap H)rightarrow B/(Bcap AH)$, $Big(a(Acap H),b(Bcap H)Big)mapsto b(Bcap AH) $?


      2. Is this bundle trivial? What are the sections?




      algebraic-topology lie-groups topological-groups fiber-bundles




      share|cite|improve this question











      Let $G$ be a connected topological group. Let $A,B$ be two closed normal subgroups such that $A$ is central. Suppose $Acap B=e$ and $G=Atimes B$ . Let $H$ be a closed subgroup. Consider the principal fiber bundle $pi: G/Hrightarrow G/AH$.



      1. Can we reduce the situation to $ A/(Acap H)times B/(Bcap H)rightarrow B/(Bcap AH)$, $Big(a(Acap H),b(Bcap H)Big)mapsto b(Bcap AH) $?


      2. Is this bundle trivial? What are the sections?





      algebraic-topology lie-groups topological-groups fiber-bundles





      share|cite|improve this question










      share|cite|improve this question




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      asked Jul 24 at 9:08









      Ronald

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