Connected components of Isom(H3)-representations of non-orientable surfaces
Let N denote the closed non-orientable surface of genus k. In this paper we study the behaviour of the 'square map' from the group of isometries of hyperbolic 3-space to the subgroup of orientation preserving isometries. The properties of the 'square map' and other related maps s...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:258269 |
| Acceso en línea: | https://ddd.uab.cat/record/258269 https://dx.doi.org/urn:doi:10.1007/s10711-022-00682-x |
| Access Level: | acceso abierto |
| Palabra clave: | Representation varieties Stiefel-Whitney class Orientation reversing isometries of H3 |
| Sumario: | Let N denote the closed non-orientable surface of genus k. In this paper we study the behaviour of the 'square map' from the group of isometries of hyperbolic 3-space to the subgroup of orientation preserving isometries. The properties of the 'square map' and other related maps serve as a technical step towards the counting of the connected components of the variety of representations of π(N) in Isom(H). We show that the variety of representations hom(π(N), Isom (H)) has 2 connected components, which are distinguished by the Stiefel-Whitney classes of the associated flat bundle. |
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