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 $\paren {n + 1}$-dimensional topological 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.