#### Volume 6, issue 3 (2006)

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Intrinsic linking and knotting of graphs in arbitrary 3–manifolds

### Erica Flapan, Hugh Howards, Don Lawrence and Blake Mellor

Algebraic & Geometric Topology 6 (2006) 1025–1035
 arXiv: math.GT/0508004
##### 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 ${S}^{3}$.

##### Keywords
intrinsically linked graphs, intrinsically knotted graphs, 3–manifolds
##### Mathematical Subject Classification 2000
Primary: 05C10, 57M25