On hyperbolic cone metrics, PSL(2, R)-character varieties, and branched coverings
Abstract/Contents
- Abstract
- We study hyperbolic cone metrics on closed surfaces whose cone angles are integer multiples of 2 pi. The first part of this thesis focuses on local deformations of these cone metrics. We show that these cone metrics depend smoothly on their underlying complex structures and conical data, and that their holonomy representations define a smooth submersion to the PSL(2, R)-character variety. Furthermore, given any tangent vector in the image of this submersion, we construct a natural horizontal lift to the space of hyperbolic cone metrics and describe this lift in terms of harmonic forms and holomorphic quadratic differentials. The second part of this thesis focuses on hyperbolic cone metrics with a prescribed holonomy representation of Euler class 2 - 2g + 1. We study the space of these cone metrics when the prescribed holonomy representation is discrete, and describe a connection between the topology of this space and the Birman-Hilden lifting properties of branched coverings between closed surfaces.
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 | 2021; ©2021 |
| Publication date | 2021; 2021 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Nguyen, Dat Pham |
|---|---|
| Degree supervisor | Kerckhoff, Steve |
| Thesis advisor | Kerckhoff, Steve |
| Thesis advisor | Danciger, Jeffrey |
| Thesis advisor | Trettel, Steve J, 1990- |
| Degree committee member | Danciger, Jeffrey |
| Degree committee member | Trettel, Steve J, 1990- |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Dat Nguyen. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2021. |
| Location | https://purl.stanford.edu/gw405rz9311 |
Access conditions
- Copyright
- © 2021 by Dat Pham Nguyen
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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