Expansion Complexes for Finite Subdivision Rules I
J. W. Cannon, W. J. Floyd, and W. R. Parry
This paper develops the basic theory of conformal structures on finite
subdivision rules. The work depends heavily on the use of expansion
complexes, which are defined and discussed in detail. It is proved that
finite subdivision rule with bounded valence and mesh approaching 0 is
conformal (in the combinatorial sense) if there is a conformal structure
the model subdivision complex with respect to which the subdivision map
conformal. This gives a new approach to the difficult combinatorial
of determining when a finite subdivision rule is conformal.
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