A Hyperbolic Surface With A Square Grid Net

Details A Hyperbolic Surface With A Square Grid Net A Hyperbolic Surface With A Square Grid Net

2004-09-28

arxiv.org/abs/math/0409560v3

Mathematics

Complex Variables

9 pages, 4 figures; section 2 has been simplified and shortened; one figure added

Scientific paper

We prove the existence of a hyperbolic surface spread over the sphere for
which the projection map has all its singular values on the extended real line,
and such that the preimage of the extended real line under the projection map
is homeomorphic to the square grid in the plane. This answers a question raised
by \`E. B. Vinberg.

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