# manifold bounded by compact manifold with $b_1=0$

Let $$X$$ be a non-compact manifold without boundary. Suppose that $$b_1(X)=0$$. Suppose $$Y$$ is a codimension zero compact submanifold with corner.

Q Can we find a compact submanifold $$Z$$ with smooth boundary such that $$Y\subset Z\subset X$$ and $$b_1(Z)=0$$.

• Can you tell us please what or where the boundary of $Z$ should be? – Sebastian Goette Sep 13 at 23:26