Constructing subdivision rules from alternating links

Rushton, Brian

doi:10.1090/S1088-4173-09-00205-7

Constructing subdivision rules from alternating links
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by Brian Rushton

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

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

Published electronically: January 5, 2010

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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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