A compact Riemann surface can be realized as a quotient space $\mathcal/\Gamma$, where $\mathcal$ is the sphere $\Sigma$, the euclidian plane $\mathbb$ or the hyperbolic plane $\mathcal$ and $\Gamma$ is a discrete group of automorphisms. This induces a covering $p:\mathcal\rightarrow\mathcal/\Gamma$. For each $\Gamma$ acting on $\mathcal$ we have a polygon $P$ such that $\mathcal$ is tesselated by $P$ under the actions of the elements of $\Gamma$. On the other hand if $P$ is a hyperbolic polygon with a side pairing satisfying certain conditions, then the group $\Gamma$ generated by the side pairing is discrete and $P$ tesselates $\mathcal$ under $\Gamma$.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:liu-7968 |
| Date | January 2006 |
| Creators | Bartolini, Gabriel |
| Publisher | Linköpings universitet, Matematiska institutionen, Matematiska institutionen |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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