Skip to main content
1 of 2

Knots in 3-manifolds

Consider a closed 3-manifold M and a knot K in M.

Is it necessarily true that pi_2 (M \setminus K) = 0?

If not, are there any conditions on M and/or K to ensure the above 2nd homotopy group of the knot complement is trivial?

Thanks!

(Note: This is of course true when M is simply connected --> S^3)