Date of Final Oral Examination (Defense)
Type of Culminating Activity
Master of Science in Mathematics
Jens Harlander, Ph.D.
Uwe Kaiser, Ph.D.
Zachariah Teitler, Ph.D.
Let Γ be a directed graph. The directed forest complex, DF(Γ), is a simplicial complex whose vertices are the edges of Γ and whose simplices are sets of edges that form a directed forest in Γ. We study the directed forest complex of Cayley graphs of finite groups. The homology of DF(Γ) contains information about the graph, Γ and about the group, G. The ultimate goal is to classify DF(Γ) up to homotopy, compute its homology, and interpret the findings in terms of properties of DF(Γ). In this thesis, we present progress made toward this goal.
Courtney, Kennedy, "The Directed Forest Complex of Cayley Graphs" (2020). Boise State University Theses and Dissertations. 1684.