Three manifolds as geometric branched coverings of the three sphere

Brumfiel, G.; Hilden, H.; Lozano, M. T.; Montesinos--Amilibia, J. M.; Ramirez--Losada, E.; Short, H.; Tejada, D.; Toro, M.

Three manifolds as geometric branched coverings of the three sphere

Authors

Brumfiel, G.

Hilden, H.

Lozano, M. T.

Montesinos--Amilibia, J. M.

Description

One method for obtaining every closed orientable 3-manifold is as branched covering of the 3-sphere over a link. There is a classical topological result showing that the minimun possible number of sheets in the covering is three. In this paper we obtain a geometric version of this result. The interest is given by the growing importance of geometry in 3-manifolds theory.
18 pages, 24 figures