Poincaré's theorem for the modular group of real Riemann surfaces
| dc.creator | Costa, Antonio F. | |
| dc.creator | Natanzon, Sergey | |
| dc.date | 2006-02-19 | |
| dc.date | 2006-09-14 | |
| dc.date.accessioned | 2026-07-07T07:03:35Z | |
| dc.date.available | 2026-07-07T07:03:35Z | |
| dc.description | Let $Mod_{g}$ be the modular group of surfaces of genus $g$. Each element $[h]\in Mod_{g}$ induces in the integer homology of a surface of genus $g$ a symplectic automorphism $H([h])$ and Poincaré shown that $H:Mod_{g}\to Sp(2g,\mathbb{Z})$ is an epimorphism. The theory of real algebraic curves justify the definition of real Riemann surface as a Riemann surface $S$ with an anticonformal involution $σ$. Let $(S,σ)$ be a real Riemann surface, the subgroup $Mod_{g}^σ$ of $Mod_{g}$ that consists of the elements $[h]\in Mod_{g}$ that have a representant $h$ such that $h\circσ=σ\circ h$, plays the rôle of the modular group in the theory of real Riemann surfaces. In this work we describe the image by $H$ of $Mod_{g}^σ$. Such image depends on the topological type of the involution $σ$. | |
| dc.description | 17 pages, LaTex | |
| dc.identifier | https://arxiv.org/abs/math/0602413 | |
| dc.identifier | http://arxiv.org/abs/math/0602413 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109028 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Poincaré's theorem for the modular group of real Riemann surfaces | |
| dc.type | text |