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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 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.

Keywords
intrinsically linked graphs, intrinsically knotted graphs, 3–manifolds
Mathematical Subject Classification 2000
Primary: 05C10, 57M25
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Publication
Received: 25 October 2005
Revised: 3 May 2006
Accepted: 11 May 2006
Published: 9 August 2006
Authors
Erica Flapan
Department of Mathematics
Pomona College
% Claremont, CA 91711
USA
Hugh Howards
Department of Mathematics
Wake Forest University
% Winston-Salem, NC 27109
USA
Don Lawrence
Department of Mathematics
Occidental College
% Los Angeles, CA 90041
USA
Blake Mellor
Department of Mathematics
Loyola Marymount University
% Los Angeles, CA 90045
USA