Convex projective geometrically finite structures
Abstract/Contents
- Abstract
- In this thesis, we explore two phenomena involving geometrically finite hyperbolic manifolds, and extend them to convex projective geometry. The first phenomenon involves the limit set of a Zariski dense geometrically finite structure. Greenberg studied limit sets of geometrically finite hyperbolic manifolds in order to understand their commensurators, and Mj extended his result to symmetric spaces. We extend this line of results to convex projective geometry, where our motivation is to understand when two geometrically finite structures define similar limit sets. We show that, when the limit of a Zariski dense geometrically finite structure is not the entire boundary at infinity, it determines the structure up to a finite index. The second phenomenon involves the characterization of geometrically finite structures. We introduce the notion of generalized geometrically finite structures, following the works of Danciger-Guéritaud-Kassel on convex cocompactness and Ballas-Cooper-Leitner on generalized cusps. We show an equivalence between a geometric and a dynamical description of such structures, similar to Bowditch's work on geometrically finite hyperbolic manifolds
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2020; ©2020 |
| Publication date | 2020; 2020 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Wolf, Adva |
|---|---|
| Degree committee member | Danciger, Jeffrey |
| Degree committee member | Trettel, Steve J, 1990- |
| Thesis advisor | Danciger, Jeffrey |
| Thesis advisor | Trettel, Steve J, 1990- |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Adva Wolf |
|---|---|
| Note | Submitted to the Department of Mathematics |
| Thesis | Thesis Ph.D. Stanford University 2020 |
| Location | electronic resource |
Access conditions
- Copyright
- © 2020 by Adva Wolf
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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