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Title page for ETD etd-03252013-161827

Type of Document Dissertation
Author Camp, Wes Alan
Author's Email Address w.camp@vanderbilt.edu
URN etd-03252013-161827
Title Graph Separators and Boundaries of Right-Angled Artin and Coxeter Groups
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Michael Mihalik Committee Chair
John Ratcliffe Committee Member
Mark Sapir Committee Member
Senta Greene Committee Member
Steven Tschantz Committee Member
  • geometric group theory
Date of Defense 2013-03-21
Availability unrestricted
We examine the connection between some vertex separators of graphs and topological properties of CAT(0) spaces acted on geometrically by groups corresponding to graphs.

For right-angled Coxeter groups with no $^3$ subgroups (three-flats), we show that the boundary of any CAT(0) space such a group acts on geometrically is locally connected if and only if the presentation graph of the group lacks a certain type of vertex separator. It was known that the presence of such a separator in the presentation graph of any right-angled Coxeter group implies that any boundary of the group is non-locally connected, and so this result fully classifies the right-angled Coxeter groups with no three-flats and locally connected boundary.

For right-angled Artin groups, we show that the presence of a type of vertex separator in the presentation graph of the group guarantees that the standard CAT(0) cube complex on which the group acts geometrically has non-path-connected boundary.

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