Complex Hyperbolic Structures on Disc Bundles over Surfaces. II. Example of a Trivial Bundle
| dc.creator | Anan'in, Sasha | |
| dc.creator | Gusevskii, Nikolay | |
| dc.date | 2005-12-17 | |
| dc.date | 2007-02-23 | |
| dc.date.accessioned | 2026-07-07T07:48:10Z | |
| dc.date.available | 2026-07-07T07:48:10Z | |
| dc.description | This article is based on the methods developed in [AGG]. We construct a complex hyperbolic structure on a trivial disc bundle over a closed orientable surface $Σ$ (of genus 2) thus solving a long standing problem in complex hyperbolic geometry (see [Gol1, p. 583] and [Sch, p. 14]). This example answers also [Eli, Open Question 8.1] if a trivial circle bundle over a closed surface of genus >1 admits a holomorphically fillable contact structure. The constructed example M satisfies the relation $2(χ+e)=3τ$ which is necessary for the existence of a holomorphic section of the bundle, where $χ=χΣ$ stands for the Euler characteristic of $Σ$, e=eM, for the Euler number of the bundle, and $τ$, for the Toledo invariant. (The relation is also valid for the series of examples constructed in [AGG].) Open question: Does there exist a holomorphic section of the bundle M? | |
| dc.description | 19 pages, 6 figures, 9 references. Changes: revised exposition | |
| dc.identifier | https://arxiv.org/abs/math/0512406 | |
| dc.identifier | http://arxiv.org/abs/math/0512406 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124404 | |
| dc.subject | Geometric Topology | |
| dc.subject | Differential Geometry | |
| dc.subject | 57S30 (Primary) 30F35, 51M10, 57M50 (Secondary) | |
| dc.title | Complex Hyperbolic Structures on Disc Bundles over Surfaces. II. Example of a Trivial Bundle | |
| dc.type | text |