Knotting and linking in spatial graph embeddings

Start: 12/07/2016 - 4:15pm
End  : 12/07/2016 - 5:15pm


Kenji Kozai (HMC)


An abstract graph can be realized (embedded) in 3-dimensional space by associating vertices to a point in space and edges between vertices as an arc between the associated points. A given graph has infinitely many embeddings, and some embeddings may be more complicated than others. One way of measuring how complicated an embedding is is to consider the knotting and linking of cycles in the graph embedding. I will give an introduction to some elementary knot and link invariants, and then show how they can be used to prove that certain graphs are intrinsically linked or knotted, that is every embedding has a non-trivial link or knot. In addition, I will discuss random knot and graph embedding models as well as what can be said about "typical" embedding of graphs.

Kravis Lower Court, Claremont McKenna College