On the Dimension of Group Boundaries

dc.contributor.advisor	Craig Guilbault
dc.contributor.committeemember	Craig Guilbault
dc.contributor.committeemember	Boris Okun
dc.contributor.committeemember	Fredric Ancel
dc.contributor.committeemember	Allen Bell
dc.contributor.committeemember	Peter Hinow
dc.creator	Moran, Molly Ann
dc.date.accessioned	2025-01-16T20:07:03Z
dc.date.available	2025-01-16T20:07:03Z
dc.date.issued	2015-05-01
dc.description.abstract	The goal of this dissertation is to find connections between the small-scale dimension (i.e. covering dimension and linearly controlled dimension) of group boundaries and the large scale dimension (i.e. asymptotic dimension and macroscopic dimension) of the group. We first show that generalized group boundaries must have finite covering dimension by using finite large-scale dimension of the space. We then restrict our attention to CAT(0) group boundaries and develop metrics on the boundary that allow us to study the linearly controlled dimension. We then obtain results relating the linearly controlled dimension of CAT(0) boundaries to the large scale dimension of the CAT(0) space.
dc.identifier.uri	http://digital.library.wisc.edu/1793/88801
dc.relation.replaces	https://dc.uwm.edu/etd/900
dc.subject	Cat(0) Space
dc.subject	Group Boundary
dc.subject	Visual Boundary
dc.subject	Z-Boundary
dc.subject	Z-Structure
dc.title	On the Dimension of Group Boundaries
dc.type	dissertation
thesis.degree.discipline	Mathematics
thesis.degree.grantor	University of Wisconsin-Milwaukee
thesis.degree.name	Doctor of Philosophy

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