Higher-rank generalizations of convex cocompact and geometrically finite dynamics

Simple item page
dc.contributor.advisorDanciger, Jeffrey
dc.contributor.committeeMemberAllcock, Daniel
dc.contributor.committeeMemberBowen, Lewis
dc.contributor.committeeMemberBallas, Samuel
dc.creatorWeisman, Theodore Joseph
dc.creator.orcid0000-0002-9396-4305
dc.date.accessioned2022-09-20T20:02:18Z
dc.date.available2022-09-20T20:02:18Z
dc.date.created2022-08
dc.date.issued2022-06-29
dc.date.submittedAugust 2022
dc.date.updated2022-09-20T20:02:19Z
dc.description.abstractWe study several higher-rank generalizations of the dynamical behavior of convex cocompact groups in rank-one Lie groups, in the context of both convex projective geometry and relatively hyperbolic groups. Our results include a dynamical characterization of a notion of convex cocompact projective structure due to Danciger-Guéritaud-Kassel. This generalizes a dynamical characterization of Anosov representations of hyperbolic groups. Using topological dynamics, we also define a new notion of geometrical finiteness in higher rank which generalizes previous notions of relative Anosov representation due to Kapovich-Leeb and Zhu. We prove that these “extended geometrically finite” representations are stable under certain small relative deformations, and we provide various examples coming from the theory of convex projective structures.
dc.description.departmentMathematics
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/2152/115842
dc.identifier.urihttp://dx.doi.org/10.26153/tsw/42740
dc.language.isoen
dc.subjectGeometric topology
dc.subjectGroup theory
dc.subjectLie groups
dc.subjectAnosov representations
dc.titleHigher-rank generalizations of convex cocompact and geometrically finite dynamics
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorThe University of Texas at Austin
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

Access full-text files

Original bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
WEISMAN-DISSERTATION-2022.pdf
Size:
2.14 MB
Format:
Adobe Portable Document Format
Download

License bundle

Now showing 1 - 2 of 2
No Thumbnail Available
Name:
PROQUEST_LICENSE.txt
Size:
4.46 KB
Format:
Plain Text
Description:
Download
No Thumbnail Available
Name:
LICENSE.txt
Size:
1.85 KB
Format:
Plain Text
Description:
Download

Collections

UT Electronic Theses and Dissertations