Constructing subdivision rules from alternating links

Author:
Brian Rushton

Journal:
Conform. Geom. Dyn. **14** (2010), 1-13

MSC (2010):
Primary 57M50

Published electronically:
January 5, 2010

MathSciNet review:
2579862

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Abstract | References | Similar Articles | Additional Information

Abstract: The study of geometric group theory has suggested several theorems related to subdivision tilings that have a natural hyperbolic structure. However, few examples exist. We construct subdivision tilings for the complement of every nonsingular, prime alternating link. These tilings define a combinatorial space at infinity, similar to the space at infinity for word hyperbolic groups.

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tilepack.c, tilepackhistory.c, subdivide.c and subdividehistory.c.

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Alternating links and subdivision rules.

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Circlepack.

Software, available from http://www.math.utk.edu/kens.

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Additional Information

**Brian Rushton**

Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah 84602

Email:
brirush@gmail.com

DOI:
https://doi.org/10.1090/S1088-4173-09-00205-7

Received by editor(s):
August 6, 2009

Published electronically:
January 5, 2010

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.