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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747

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

DOI: 10.2140/agt.2006.6.1025

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

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

USA
Hugh Howards
Department of Mathematics
Wake Forest University

USA
Don Lawrence
Department of Mathematics
Occidental College

USA
Blake Mellor
Department of Mathematics
Loyola Marymount University

USA