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Full-Text Articles in Algebraic Geometry
Intrinsic Linking And Knotting Of Graphs In Arbitrary 3–Manifolds, Erica Flapan, Hugh Howards, Don Lawrence, Blake Mellor
Intrinsic Linking And Knotting Of Graphs In Arbitrary 3–Manifolds, Erica Flapan, Hugh Howards, Don Lawrence, Blake Mellor
Pomona Faculty Publications and Research
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.
Intrinsic Knotting And Linking Of Complete Graphs, Erica Flapan
Intrinsic Knotting And Linking Of Complete Graphs, Erica Flapan
Pomona Faculty Publications and Research
We show that for every m∈N, there exists an n∈N such that every embedding of the complete graph Kn in R3 contains a link of two components whose linking number is at least m. Furthermore, there exists an r∈N such that every embedding of Kr in R3 contains a knot Q with |a2(Q)| ≥ m, where a2(Q) denotes the second coefficient of the Conway polynomial of Q.