|
Título:
|
Three manifolds as geometric branched coverings of the three sphere.
|
|
Autores:
|
Brumfield, G. ;
Hilden, Hugh Michael ;
Lozano Imízcoz, María Teresa ;
Montesinos Amilibia, José María ;
Ramírez Losada, E. ;
Short, H. ;
Tejada Cazorla, Juan Antonio ;
Toro, M.
|
|
Tipo de documento:
|
texto impreso
|
|
Editorial:
|
Sociedad Matemática Mexicana, 2008-10
|
|
Dimensiones:
|
application/pdf
|
|
Nota general:
|
info:eu-repo/semantics/restrictedAccess
|
|
Idiomas:
|
|
|
Palabras clave:
|
Estado = Publicado
,
Materia = Ciencias: Matemáticas: Topología
,
Tipo = Artículo
|
|
Resumen:
|
A finite covolume, discrete group of hyperbolic isometries U, acting on H3, is said to be universal if for every closed orientable 3-manifold M3 there is a finite index subgroup G of U so that M3=H3/G. It has been shown [H. M. Hilden et al., Invent. Math. 87 (1987), no. 3, 441–456;] that the orbifold group U of the Borromean rings with singular angle 90 degrees is universal and that H3/U=S3. In the present paper the authors construct a sequence of hyperbolic orbifold structures on S3 with orbifold groups Gi, i=1,…,4, such that G?G1?G2?G3?G4?U and they use this to obtain the following geometric branched covering space theorem: Let M3 be a closed orientable 3-manifold. Then there are finite index subgroups G?G1 of U such that M3=H3/G, S3=H3/G1 and the inclusion G?G1 induces a 3-fold simple branched covering M3?S3.
The group U acts as a group of isometries of hyperbolic 3-space H3 so that there is a tessellation of H3 by regular dodecahedra any one of which is a fundamental domain for U. The authors construct a closely related Euclidean crystallographic group Uˆ corresponding to a tessellation of E3 by cubes that are fundamental domains for Uˆ, and exhibit a homomorphism ?:U?Uˆ which defines a branched covering H3?E3 that respects the two tessellations. They classify the finite index subgroups of Uˆ, and use their pullback under ? to obtain the main result of the paper: For any positive integer n there is an index n subgroup of U generated by rotations.
|
|
En línea:
|
https://eprints.ucm.es/id/eprint/22006/1/montesinos40.pdf
|
