Definition of a 3-cobordism (in my context) is a pair $(M, \partial_{-} M, \partial_{+}M)$, where $M$ is a closed orientable topological 3-manifold and $\partial M$ is a disjoint union of $\partial_{-} M$ and $\partial_{+}M)$.
I have a question regarding the following sentence:
"$(W, U, V)$ is a 4-dimensional cobordism with boundary $(M, \partial_{-} M, \partial_{+}M)$."
Here $W$ is a 4-dimensional manifold and $U, V$ are 3 dimensional manifolds.
What is the definition of 4-dimensional cobordism used here? Is it just same as the 3-dimensional case? That is, $\partial W$ is a disjoint union of $U$ and $V$.
Also what is the definition of the term boundary used above?