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Behavior of geodesic rays in spaces with geometric group actions
Descriptive
TypeOfResource
Text
TitleInfo
(ID = T-1)
Title
Behavior of geodesic rays in spaces with geometric group actions
Identifier
ETD_2557
Identifier
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http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000053495
Language
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eng
Genre
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theses
Subject
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Topic
Mathematics
Subject
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(authority = ETD-LCSH)
Topic
Geodesics (Mathematics)
Subject
(ID = SBJ-3);
(authority = ETD-LCSH)
Topic
G-spaces
Abstract
(type = abstract)
This dissertation studies certain groups by studying spaces on which they act geometrically. These spaces are studied by examining the behavior of geodesic rays in these spaces, which gives geometric data about the space that can translate into algebraic data about the group. First, we investigate the amenability of Thompson's group F by studying the geometry of its Cayley graph. We apply the uniformly finite homology of Block and Weinberger to subsets of this graph. Many large subsets of the Cayley graph are shown to be nonamenable by exhibiting certain arrangements of geodesic rays which we call "tree-like quasi-covers". We then examine CAT(0) boundaries. If a group acts geometrically on two CAT(0) spaces X and Y , then one obtains a G-equivariant quasi-isometry from X to Y. One may look at the image of a geodesic ray in X, and look at its closure in the boundary of Y . We show that this "boundary image" can have the homeomorphism type of any compact, connected subset of Euclidean space.
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electronic resource
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v, 63 p. : ill.
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Note
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Ph.D.
Note
Includes abstract
Note
Vita
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(type = bibliography)
Includes bibliographical references
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by Daniel Staley
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Staley
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Daniel
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1983-
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author
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Daniel Staley
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Steven
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chair
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Steven Ferry
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Luo
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Feng
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internal member
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Feng Luo
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Rong
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Xiaochun
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Xiaochun Rong
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Ruane
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Kim
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Kim Ruane
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Rutgers University
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degree grantor
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Graduate School - New Brunswick
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school
OriginInfo
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2010
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2010
Place
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xx
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
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ETD
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Title
Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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NjNbRU
Identifier
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doi:10.7282/T3ZC82W3
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ETD doctoral
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Rights
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The author owns the copyright to this work.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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Name
FamilyName
Staley
GivenName
Daniel
Role
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DateTime
2010-04-08 14:33:37
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Daniel Staley
Affiliation
Rutgers University. Graduate School - New Brunswick
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Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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ETD
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