Tubular neighborhood of knot

293 Views Asked by At

Is it always true that a tubular neighborhood of a knot $K \subset M$, where $M$ is a generic smooth 3-manifold, is diffeomorphic to $S^1 \times B^2$ (if you prefer diffeomorphic to $S^1 \times \mathbb{R}^2$, I just find $B^2$ more intuitive), where $B^2$ denotes the interior of $D^2$? If yes, why? I know that all tubular neighborhoods are unique up to isotopy, but I cannot figure out if this helps me.