Geodesic
Intrinsic linking and knotting of graphs in arbitrary 3–manifolds
Flapan, Erica1 ; Howards, Hugh2 ; Lawrence, Don3 ; Mellor, Blake4
1Department of Mathematics, Pomona College, % Claremont, CA 91711, USA
2Department of Mathematics, Wake Forest University, % Winston-Salem, NC 27109, USA
3Department of Mathematics, Occidental College, % Los Angeles, CA 90041, USA
4Department of Mathematics, Loyola Marymount University, % Los Angeles, CA 90045, USA
Algebraic and Geometric Topology, Tome 6 (2006) no. 3, pp. 1025-1035
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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.

DOI : 10.2140/agt.2006.6.1025
Keywords: intrinsically linked graphs, intrinsically knotted graphs, 3–manifolds

Flapan, Erica  1   ; Howards, Hugh  2   ; Lawrence, Don  3   ; Mellor, Blake  4

1 Department of Mathematics, Pomona College, % Claremont, CA 91711, USA
2 Department of Mathematics, Wake Forest University, % Winston-Salem, NC 27109, USA
3 Department of Mathematics, Occidental College, % Los Angeles, CA 90041, USA
4 Department of Mathematics, Loyola Marymount University, % Los Angeles, CA 90045, USA 
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Flapan, Erica; Howards, Hugh; Lawrence, Don; Mellor, Blake. Intrinsic linking and knotting of graphs in arbitrary 3–manifolds. Algebraic and Geometric Topology, Tome 6 (2006) no. 3, pp. 1025-1035. doi: 10.2140/agt.2006.6.1025

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