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±