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Expansion complexes for finite subdivision rules. I
Author(s):
J.
W.
Cannon;
W.
J.
Floyd;
W.
R.
Parry
Journal:
Conform. Geom. Dyn.
10
(2006),
63-99.
MSC (2000):
Primary 30F45, 52C20;
Secondary 20F67, 52C26
Posted:
March 22, 2006
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Abstract:
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 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.
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Additional Information:
J.
W.
Cannon
Affiliation:
Department of Mathematics Brigham Young University, Provo, Utah 84602
Email:
cannon@math.byu.edu
W.
J.
Floyd
Affiliation:
Department of Mathematics Virginia Tech, Blacksburg, Virginia 24061
Email:
floyd@math.vt.edu
W.
R.
Parry
Affiliation:
Department of Mathematics Eastern Michigan University, Ypsilanti, Michigan 48197
Email:
walter.parry@emich.edu
DOI:
10.1090/S1088-4173-06-00126-3
PII:
S 1088-4173(06)00126-3
Keywords:
Conformality,
expansion complex,
finite subdivision rule
Received by editor(s):
November 22, 2004
Posted:
March 22, 2006
Additional Notes:
This research was supported in part by NSF grants DMS-9803868, DMS-9971783, DMS-10104030, and DMS-0203902
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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