Intrinsic linking and knotting of graphs in arbitrary 3–manifolds

Abstract

We prove that a graph is intrinsically linked in an arbitrary 3–manifold $M$ if and only if it is intrinsically linked in $S^3$. Also, assuming the Poincaré Conjecture, we prove that a graph is intrinsically knotted in $M$ if and only if it is intrinsically knotted in $S^3$.