What is the base space and fibre in the construction of double disk bundle? Double disk bundle: A smooth, closed manifold M ∼= DB− ∪_L DB+ where · B±, L smooth, closed manifolds · Dℓ±+1 → DB± → B± smooth disk bundles such that Sℓ± → L ∼= ∂DB− ∼= ∂DB+ → B±