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This question asks whether every circle bundle comes from a 2 plane bundle. Paracompact space please - preferably a manifold.
By circle bundle I mean the usual thing, a fiber bundle with fiber, a circle, that is locally a product bundle. The transition functions lie in some group of homeomorphisms of the circle.
A similar question can be asked for a sphere bundle.
By circle bundle I mean the usual thing, a fiber bundle with fiber, a circle, that is locally a product bundle. The transition functions lie in some group of homeomorphisms of the circle.
A similar question can be asked for a sphere bundle.