Intrinsic linking and knotting of graphs in arbitrary 3–manifolds

Authors

Erica Flapan
Hugh Howards
Don Lawrence
Blake Mellor, Loyola Marymount UniversityFollow

Document Type

Article

Publication Date

2006

Abstract

We prove that a graph is intrinsically linked in an arbitrary 3–manifold MM 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.

Original Publication Citation

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.

Publisher Statement

Permission has been granted by Mathematical Sciences Publishers to supply this article for educational and research purposes. More info can be found about the Algebraic & Geometric Topology at http://msp.org/agt/about/journal/about.html. © Mathematical Sciences Publishers.

Digital Commons @ LMU & LLS Citation

Flapan, Erica; Howards, Hugh; Lawrence, Don; and Mellor, Blake, "Intrinsic linking and knotting of graphs in arbitrary 3–manifolds" (2006). Mathematics, Statistics and Data Science Faculty Works. 41.
https://digitalcommons.lmu.edu/math_fac/41