Definition:Cobordism/Oriented

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

An oriented cobordism $W^{n+1}$ is an $(n+1)$-dimensional manifold such that:
 * $\partial W = X \cup \overline Y$

where:
 * $\partial W$ denotes the boundary of $W$
 * $\overline Y$ denotes $Y$ taken with reverse orientation.