Double disk bundle: A smooth, closed manifold $M \cong DB^{-} \cup_L DB^{+}$ where · $B^{±}, L$ smooth, closed manifolds · $D^{l± +1} → DB^{±} → B^{±}$ smooth disk bundles such that $S^{l±} → L \cong ∂DB^{−} \cong ∂DB^{+} → B^{±}$ is sphere bundle. In the above Double disk bundle, I do not understand what is base space and fibre of a double disk bundle are.

Double disk bundle: A smooth, closed manifold $M \cong DB^{-} \cup_L DB^{+}$ where · $B^{±}, L$ smooth, closed manifolds · $D^{l± +1} → DB^{±} → B^{±}$ smooth disk bundles such that $S^{l±} → L \cong ∂DB^{−} \cong ∂DB^{+} → B^{±}$ is sphere bundle. In the above Double disk bundle, I do not understand what is base space and fibre of a double disk bundle are. Please give some ideas to understand.

Thanks

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±

Double disk bundle: A smooth, closed manifold $M \cong DB^{-} \cup_L DB^{+}$ where · $B^{±}, L$ smooth, closed manifolds · $D^{l± +1} → DB^{±} → B^{±}$ smooth disk bundles such that $S^{l±} → L \cong ∂DB^{−} \cong ∂DB^{+} → B^{±}$ is sphere bundle. In the above Double disk bundle, I do not understand what is base space and fibre of a double disk bundle are.