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Ziggurat fringes are self-similar
Published online by Cambridge University Press: 28 December 2015
Abstract
We give explicit formulae for fringe lengths of the Calegari–Walker ziggurats—i.e., graphs of extremal rotation numbers associated with 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, Calegari and Walker.
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- © Cambridge University Press, 2015
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