## Expansion complexes for finite subdivision rules. I

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- by J. W. Cannon, W. J. Floyd and W. R. Parry
- Conform. Geom. Dyn.
**10**(2006), 63-99 - DOI: https://doi.org/10.1090/S1088-4173-06-00126-3
- Published electronically: 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.## References

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## Bibliographic 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
- MR Author ID: 67750
- Email: floyd@math.vt.edu
**W. R. Parry**- Affiliation: Department of Mathematics Eastern Michigan University, Ypsilanti, Michigan 48197
- MR Author ID: 136390
- Email: walter.parry@emich.edu
- Received by editor(s): November 22, 2004
- Published electronically: March 22, 2006
- Additional Notes: This research was supported in part by NSF grants DMS-9803868, DMS-9971783, DMS-10104030, and DMS-0203902
- © Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn.
**10**(2006), 63-99 - MSC (2000): Primary 30F45, 52C20; Secondary 20F67, 52C26
- DOI: https://doi.org/10.1090/S1088-4173-06-00126-3
- MathSciNet review: 2218641