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Ziggurat fringes are self-similar

Published online by Cambridge University Press:  28 December 2015

SUBHADIP CHOWDHURY
SUBHADIP CHOWDHURY*
Affiliation:
Department of Mathematics, University of Chicago, Chicago, IL 60637, USA email subhadip@math.uchicago.edu
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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 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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 3 , May 2017 , pp. 739 - 757
Copyright
© Cambridge University Press, 2015 

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