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arXiv · 1503.04227

Ziggurat fringes are self-similar

Subhadip Chowdhury
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Abstract

We give explicit formulae for fringe lengths of the Calegari-Walker Ziggurats -- i.e. graphs of extremal rotation numbers associated to positive words in free groups. These formulae reveal (partial) integral projective self-similarity in ziggurat fringes, which are low-dimensional projections of characteristic polyhedra on the bounded cohomology of free groups. This explains phenomena observed experimentally by Gordenko and Calegari-Walker.

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Subhadip Chowdhury. 2015-03-13. Ziggurat fringes are self-similar. https://doi.org/10.1017/etds.2015.75

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