Open AccessExpansion complexes for finite subdivision rules. I
Author(s) -
James Can,
William J. Floyd,
Walter Parry
Publication year - 2006
Publication title -
conformal geometry and dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.534
H-Index - 18
ISSN - 1088-4173
DOI - 10.1090/s1088-4173-06-00126-3
Subject(s) - subdivision , conformal map , subdivision surface , bounded function , computer science , mathematics , geometry , mathematical analysis , archaeology , history
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 a finite subdivision rule with bounded valence and mesh approaching 0 0 is conformal (in the combinatorial sense) if there is a partial conformal structure on the model subdivision complex with respect to which the subdivision map is conformal. This gives a new approach to the difficult combinatorial problem of determining when a finite subdivision rule is conformal.