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Topological full groups of minimal subshifts and quantifying local embeddings into finite groups

Published online by Cambridge University Press:  05 April 2022

HENRY BRADFORD*
Affiliation:
Christ’s College, University of Cambridge, St Andrew’s Street, Cambridge, CB2 3BU, UK
DANIELE DONA
Affiliation:
Einstein Institute of Mathematics, Edmond J. Safra Campus Givat Ram, The Hebrew University of Jerusalem, 9190401 Jerusalem, Israel (e-mail: daniele.dona@mail.huji.ac.il)
*

Abstract

We investigate quantitative aspects of the locally embeddable into finite groups (LEF) property for subgroups of the topological full group of a two-sided minimal subshift over a finite alphabet, measured via the LEF growth function. We show that the LEF growth of may be bounded from above and below in terms of the recurrence function and the complexity function of the subshift, respectively. As an application, we construct groups of previously unseen LEF growth types, and exhibit a continuum of finitely generated LEF groups which may be distinguished from one another by their LEF growth.

Type
Original Article
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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