Skip to main content
MathOverflow

Return to Question

format math, phrase put off by commas
Source Link
edit approved Dec 27, 2014 at 22:22
Community Bot
edit approved Dec 27, 2014 at 22:22
Community Bot
  • 1
  • 2
  • 3

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

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

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

Thanks!

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

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)

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 --> $S^3$)

Source Link
ali elgindi
ali elgindi
  • 77
  • 4

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)