Abstract
In the ring $\mathbf{Z}[\frac{1+\sqrt{5}}{2}]$, there is a natural subdivision technique analogous to regular subdivision in rational algebraic rings like $\mathbf{Z}[\frac{1}{2}]$. The properties of this subdivision process are developed using the matrix associated to the Fibonacci substitution tiling. These properties are applied to prove some finiteness properties for a discrete group of piecewise-linear homeomorphisms.
Citation
Sean Cleary. "Regular subdivision in $\mathbf{Z}[\frac{1+\sqrt{5}}{2}]$." Illinois J. Math. 44 (3) 453 - 464, Fall 2000. https://doi.org/10.1215/ijm/1256060407
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