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

Mathematics, Statistics and Data Science

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that a graph is intrinsically linked in an arbitrary 3–manifold MM if and only if it is intrinsically linked in S ³ . Also, assuming the Poincaré Conjecture, we prove that a graph is intrinsically knotted in M if and only if it is intrinsically knotted in S ³ .

Original language	English
Pages (from-to)	1025-1035
Journal	Algebraic Geometric Topology
Volume	6
State	Published - 2006

Keywords

intrinsically linked graphs
intrinsically knotted graphs
3–manifolds

Disciplines

Geometry and Topology

Cite this

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title = "Intrinsic linking and knotting of graphs in arbitrary 3–manifolds",

abstract = " We prove that a graph is intrinsically linked in an arbitrary 3–manifold MM if and only if it is intrinsically linked in S 3 . Also, assuming the Poincar{\'e} Conjecture, we prove that a graph is intrinsically knotted in M if and only if it is intrinsically knotted in S 3 .",

keywords = "intrinsically linked graphs, intrinsically knotted graphs, 3–manifolds",

author = "Erica Flapan and Hugh Howards and Don Lawrence and Blake Mellor",

note = "Flapan, E., H. Howards, D. Lawrence and B. Mellor, 2006: Intrinsic linking and knotting of graphs in arbitrary 3-manifolds. Algebr. Geom. Topol., 6, 2006, 1025-1035.",

year = "2006",

language = "English",

volume = "6",

pages = "1025--1035",

journal = "Algebraic Geometric Topology",

issn = "1472-2739",

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TY - JOUR

T1 - Intrinsic linking and knotting of graphs in arbitrary 3–manifolds

AU - Flapan, Erica

AU - Howards, Hugh

AU - Lawrence, Don

AU - Mellor, Blake

N1 - Flapan, E., H. Howards, D. Lawrence and B. Mellor, 2006: Intrinsic linking and knotting of graphs in arbitrary 3-manifolds. Algebr. Geom. Topol., 6, 2006, 1025-1035.

PY - 2006

Y1 - 2006

N2 - We prove that a graph is intrinsically linked in an arbitrary 3–manifold MM if and only if it is intrinsically linked in S 3 . Also, assuming the Poincaré Conjecture, we prove that a graph is intrinsically knotted in M if and only if it is intrinsically knotted in S 3 .

AB - We prove that a graph is intrinsically linked in an arbitrary 3–manifold MM if and only if it is intrinsically linked in S 3 . Also, assuming the Poincaré Conjecture, we prove that a graph is intrinsically knotted in M if and only if it is intrinsically knotted in S 3 .

KW - intrinsically linked graphs

KW - intrinsically knotted graphs

KW - 3–manifolds

UR - https://digitalcommons.lmu.edu/math_fac/41

M3 - Article

SN - 1472-2739

VL - 6

SP - 1025

EP - 1035

JO - Algebraic Geometric Topology

JF - Algebraic Geometric Topology

ER -

Intrinsic linking and knotting of graphs in arbitrary 3–manifolds

Abstract

Keywords

Disciplines

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Cite this