Advisors: Greg Bell Committee members: Talia Fernós; Dan Yasaki.
Özet:
We discuss large scale geometric properties of Cayley graphs of the integers using different infinite generating sets. We define the notion of k-prisms for graphs and study the large scale geometry of graphs with this property. It turns out that graphs with k-prisms for all k cannot have property A and thus are infinite dimensional in a strong sense. We give an example of an infinite family of graphs that have k-prisms for all k and we also give an example of a space the has property A and "almost has" k-prisms.