An obstruction to property A

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Christopher Neil Pritchard (Creator)
Institution
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/
Advisor
Greg Bell

Abstract: 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.

Additional Information

Publication
Thesis
Language: English
Date: 2018
Keywords
Cayley graph, Geometric group theory, k-prisms, Large scale geometry, Property A
Subjects
Geometric group theory
Metric spaces
Cayley graphs
Prisms

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