A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Soficity of free extensions of effective subshifts
Tekijät: Barbieri, Sebastian; Sablik, Mathieu; Salo, Ville
Kustantaja: AMER INST MATHEMATICAL SCIENCES-AIMS
Kustannuspaikka: SPRINGFIELD
Julkaisuvuosi: 2024
Journal: Discrete and continuous dynamical systems: series a
Tietokannassa oleva lehden nimi: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Lehden akronyymi: DISCRETE CONT DYN-A
Sivujen määrä: 33
ISSN: 1078-0947
eISSN: 1553-5231
DOI: https://doi.org/10.3934/dcds.2024125
Verkko-osoite: https://www.aimsciences.org//article/doi/10.3934/dcds.2024125
Tiivistelmä
Let G be a group and H <= G a subgroup. The free extension of an H-subshift X to G is the G-subshift Xe whose configurations are those for which the restriction to every coset of H is a configuration from X. We study the case of G = H x K for infinite and finitely generated groups H and K. On the one hand, we show that if K is nonamenable and H has decidable word problem, then the free extension to G of any H-subshift which is effectively closed is a sofic G-subshift. On the other hand, we prove that if both H and K are amenable, there are always H-subshifts which are effectively closed by patterns whose free extension to G is non-sofic. We also present a few applications in the form of a new simulation theorem and a new class of groups which admit strongly aperiodic SFTs.
Let G be a group and H <= G a subgroup. The free extension of an H-subshift X to G is the G-subshift Xe whose configurations are those for which the restriction to every coset of H is a configuration from X. We study the case of G = H x K for infinite and finitely generated groups H and K. On the one hand, we show that if K is nonamenable and H has decidable word problem, then the free extension to G of any H-subshift which is effectively closed is a sofic G-subshift. On the other hand, we prove that if both H and K are amenable, there are always H-subshifts which are effectively closed by patterns whose free extension to G is non-sofic. We also present a few applications in the form of a new simulation theorem and a new class of groups which admit strongly aperiodic SFTs.
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