intrinsic linking, intrinsic knotting, graphs, arbitrary 3-manifolds
We prove that a graph is intrinsically linked in an arbitrary 3–manifold M if and only if it is intrinsically linked in S3. Also, assuming the Poincaré Conjecture, we prove that a graph is intrinsically knotted in M if and only if it is intrinsically knotted in S3.
© 2006 Mathematical Sciences Publishers
E. Flapan, H. Howards, D. Lawrence, B. Mellor, Intrinsic Linking and Knotting in Arbitrary 3-Manifolds, Algebraic and Geometric Topology, Vol. 6, (2006) 1025-1035. doi: 10.2140/agt.2006.6.1025