Definition:Cobordism

Definitions
Let $X^n$ and $Y^n$ be manifolds without boundary of dimension $n$.

A cobordism $W^{n + 1}$ between $X$ and $Y$ is an $\paren {n + 1}$-dimensional manifold such that:
 * $\partial W = X \cup Y$

where $\partial W$ denotes the boundary of $W$.

Also denoted as
If the dimension of $X$ and $Y$ are clear, it is commonplace to omit the indices and state that $W$ is a cobordism between $X$ and $Y$.