Effective mapping class group dynamics
Abstract/Contents
- Abstract
- We prove a quantitative estimate with a power saving error term for the number of filling closed geodesics of a given topological type and length at most L on an arbitrary closed, orientable, negatively curved surface. More generally, we prove estimates of the same kind for the number of free homotopy classes of filling closed curves of a given topological type on a closed, orientable surface whose geometric intersection number with respect to a given filling geodesic current is at most L. The proofs rely on recent progress made on the study of the effective dynamics of the mapping class group on Teichmüller space and the space of closed curves of a closed, orientable surface, and introduce a novel method for addressing counting problems of mapping class group orbits that naturally yields power saving error terms. This method is also applied to study counting problems of mapping class group orbits of Teichmüller space with respect to Thurston's asymmetric metric.
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 | Arana Herrera, Francisco Andres |
|---|---|
| Degree supervisor | Kerckhoff, Steve |
| Degree supervisor | Wright, Alexander |
| Thesis advisor | Kerckhoff, Steve |
| Thesis advisor | Wright, Alexander |
| Thesis advisor | Trettel, Steve J, 1990- |
| Degree committee member | Trettel, Steve J, 1990- |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Francisco Arana-Herrera. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2021. |
| Location | https://purl.stanford.edu/pj986kf7099 |
Access conditions
- Copyright
- © 2021 by Francisco Andres Arana Herrera
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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