dc.creator | Camp, Wes Alan | |
dc.date.accessioned | 2020-08-21T21:34:14Z | |
dc.date.available | 2015-04-15 | |
dc.date.issued | 2013-04-15 | |
dc.identifier.uri | https://etd.library.vanderbilt.edu/etd-03252013-161827 | |
dc.identifier.uri | http://hdl.handle.net/1803/11306 | |
dc.description.abstract | 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. | |
dc.format.mimetype | application/pdf | |
dc.subject | geometric group theory | |
dc.title | Graph Separators and Boundaries of Right-Angled Artin and Coxeter Groups | |
dc.type | dissertation | |
dc.contributor.committeeMember | Senta Greene | |
dc.contributor.committeeMember | Mark Sapir | |
dc.contributor.committeeMember | John Ratcliffe | |
dc.contributor.committeeMember | Steven Tschantz | |
dc.type.material | text | |
thesis.degree.name | PHD | |
thesis.degree.level | dissertation | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Vanderbilt University | |
local.embargo.terms | 2015-04-15 | |
local.embargo.lift | 2015-04-15 | |
dc.contributor.committeeChair | Michael Mihalik | |