Mathematics

The end structure of an open 3-manifold captures the behavior of the manifold at infinity. We previously showed that each finitely generated Abelian group is the end homogeneity group of some 3-manifold. We discuss Cayley graphs of finitely generated groups and show how certain embeddings of these graphs in R³ may be used to extend the previous result to non-Abelian finitely generated groups.

In part 2 of this talk, I will show the connection between Cayley graphs and ends of three manifolds.