Sufficiently Rich Families of Planar Rings
J. W. Cannon, W. J. Floyd, and W. R. Parry
July 22, 1996
It has been conjectured that if $G$ is a negatively curved discrete group with
space at infinity $\partial G$ the 2-sphere, then $G$ has a properly
discontinuous, cocompact, isometric action on hyperbolic 3-space. Cannon and
Swenson reduced the conjecture to determining that a certain sequence of
coverings of $\partial G$ is conformal in the sense of Cannon's combinatorial
Riemann mapping theorem. In this paper it is proved that, in this setting, the
two axioms of conformality can be replaced by a single axiom which is implied by
each of them.
compressed PostScript file (1,100
pdf file (1,332 Kb)
Back to the list of papers .
Back to the home page of