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 $M_{2}\times \{1\}$.

Related notions

• Framed cobordism of framed submanifolds
• Oriented cobordism of oriented submanifolds