Closure of orbits of the pure mapping class group in the character variety

• 成果类型: Article
• 署名作者: Golsefidy, Alireza S.; Tamam, Nattalie
• 署名单位: University of California System; University of California San Diego
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-13583
• DOI: 10.1073/pnas.2416120122
• 发表日期: 2025-04-15
• 关键词: representation varieties; topological dynamics; MODULI SPACES; monodromy

摘要

The pure mapping class group of an oriented surface acts on the character variety of the surface. We investigate the closure of its orbits under either Zariski or analytic topologies. We show that a generic infinite orbit is dense in an open subset of the corresponding modified relative character variety. Moreover, we specify that being generic can be captured as a combination of passing to a Zariski-open subscheme and avoiding a concrete set of exceptional cases. In addition, the functorial behavior of the involved schemes is described in detail. In particular, we answer a question posed by Goldman and place the recent work of Bourgain, Gamburd, and Sarnak on Markoff triples in a more general context.