| Título: | On universal groups and three-manifolds |
| Autores: | Montesinos Amilibia, José María ; Hilden, Hugh Michael ; Lozano Imízcoz, María Teresa ; Whitten, Wilbur Carrington |
| Tipo de documento: | texto impreso |
| Editorial: | Springer-Verlag, 1987 |
| Dimensiones: | application/pdf |
| Nota general: | info:eu-repo/semantics/restrictedAccess |
| Idiomas: | |
| Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Topología , Tipo = Artículo |
| Resumen: |
Let P be a regular dodecahedron in the hyperbolic 3-space H3with the dihedral angles 90?. Choose 6 mutually disjoint edgesE1,E2,?,E6 of P such that each face of P intersects E1?E2???E6 in one edge and the opposite vertex. Let U be the group of orientation-preserving isometries of H3 generated by 90?-rotations about E1,?,E6. It was observed by W. Thurston that H3/U=S3 and that the projection H3?H3/U is a covering branched over the Borromean rings with branching indices 4. The main result of the paper is the following universality of U. Theorem: For every closed, oriented 3-manifold M there exists a subgroup G of U of finite index such that M=H3/G. In other words M is a hyperbolic orbifold finitely covering the hyperbolic orbifold H3/U. The main ingredient of the proof is the strict form of the universality of the Borromean rings (earlier obtained by the first three authors): each closed, oriented 3-manifold is shown to be a covering of S3 branched over the Borromean rings with indices 1, 2, 4. This theorem offers a new approach to the Poincaré conjecture: If M=H3/G as above and ?1(M)=1 then G is generated by elements of finite order. The authors start off an algebraic investigation of U?PSL2(C) by constructing three generators of U which are 2×2 matrices over the ring of algebraic integers in the field Q(2?,3?,5?,1?+5?,?1????). |
| En línea: | https://eprints.ucm.es/id/eprint/17162/1/Montesinos08.pdf |
Ejemplares
| Estado |
|---|
| ningún ejemplar |
