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PreprintarXiv licencearXiv

Topologically free minimal actions without dynamical comparison

  • Paolo Boldrini
  • Akshara Prasad
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Abstract

We show the existence of a topologically free minimal action of 𝔽∞ on the Cantor space that does not have dynamical comparison. Moreover, we show that this phenomenon can happen both in the presence and in the absence of invariant measures. We also show that strict comparison of the reduced crossed product C*-algebra does not imply dynamical comparison for minimal actions. Our technique involves constructing a monoid which is not almost unperforated, embedding it into a countable refinement monoid and then realising it as the type semigroup associated to a dynamical system.

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Cite

BibTeXRIS
BibTeX
@misc{boldrini2026topologically,
  title = {{Topologically free minimal actions without dynamical comparison}},
  author = {Paolo Boldrini and Akshara Prasad},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.01896},
  eprint = {2607.01896},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.01896},
}
RIS
TY  - UNPB
TI  - Topologically free minimal actions without dynamical comparison
AU  - Paolo Boldrini
AU  - Akshara Prasad
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2607.01896
UR  - https://arxiv.org/abs/2607.01896
AB  - We show the existence of a topologically free minimal action of 𝔽_∞ on the Cantor space that does not have dynamical comparison. Moreover, we show that this phenomenon can happen both in the presence and in the absence of invariant measures. We also show that strict comparison of the reduced crossed product C*-algebra does not imply dynamical comparison for minimal actions. Our technique involves constructing a monoid which is not almost unperforated, embedding it into a countable refinement monoid and then realising it as the type semigroup associated to a dynamical system.
ER  -