Intrinsic Linking and Knotting of Graphs in Arbitrary 3–manifolds

Authors

Erica Flapan, Pomona CollegeFollow
Hugh Howards
Don Lawrence
Blake Mellor, Loyola Marymount University

Document Type

Article

Department

Mathematics (Pomona)

Publication Date

2006

Keywords

intrinsic linking, intrinsic knotting, graphs, arbitrary 3-manifolds

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.

Comments

Posted with the permission of Mathematical Sciences Publishers.

Rights Information

© 2006 Mathematical Sciences Publishers

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.2140/agt.2006.6.1025

Recommended Citation

E. Flapan, H. Howards, D. Lawrence, B. Mellor, Intrinsic Linking and Knotting in Arbitrary 3-Manifolds, Algebraic and Geometric Topology, Vol. 6, (2006) 1025-1035. doi: 10.2140/agt.2006.6.1025