Sufficiently Rich Families of Planar Rings
نویسندگان
چکیده
It has been conjectured that if G is a negatively curved discrete group with space at infinity ∂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 ∂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.
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