Intrinsically linked graphs and even linking number

Details Intrinsically linked graphs and even linking number Intrinsically linked graphs and even linking number

2005-11-05

arxiv.org/abs/math/0511133v1

Algebr. Geom. Topol. 5 (2005) 1419-1432

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-55.abs.html

Scientific paper

We study intrinsically linked graphs where we require that every embedding of the graph contains not just a non-split link, but a link that satisfies some additional property. Examples of properties we address in this paper are: a two component link with lk(A,L) = k2^r, k not 0, a non-split n-component link where all linking numbers are even, or an n-component link with components L, A_i where lk(L,A_i) = 3k, k not 0. Links with other properties are considered as well. For a given property, we prove that every embedding of a certain complete graph contains a link with that property. The size of the complete graph is determined by the property in question.

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