Cobordism of submanifolds

Definition

Suppose $M_{1}$ and $M_{2}$ are submanifolds of a differential manifold $P$ . A cobordism of submanifolds from $M_{1}$ to $M_{2}$ is a submanifold with boundary $(N, \partial N)$ in $P \times I$ , that provides a cobordism between $M_{1} \times {0}$ and $M_{2} \times {1}$ .

Definition

Related notions