PreprintCC BY 4.0arXiv
Medvedev degrees of SFTs on cocompact Fuchsian groups
Abstract
We prove that for any cocompact Fuchsian group the class of Medvedev degrees attained by subshifts of finite type is the class of Π10 degrees. This result relies on the construction of a rigid hierarchical structure in a graph model of the hyperbolic plane, and on the fact that every such group admits a representation in PSL2(ℝ) such that the matrices in the image have coefficients that are computable real numbers.
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BibTeX
@misc{barbieri2026medvedev,
title = {{Medvedev degrees of SFTs on cocompact Fuchsian groups}},
author = {Sebastián Barbieri and Nicanor Carrasco-Vargas and Paul Toussaint},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04353},
eprint = {2609.04353},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04353},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Medvedev degrees of SFTs on cocompact Fuchsian groups
AU - Sebastián Barbieri
AU - Nicanor Carrasco-Vargas
AU - Paul Toussaint
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04353
UR - https://arxiv.org/abs/2609.04353
AB - We prove that for any cocompact Fuchsian group the class of Medvedev degrees attained by subshifts of finite type is the class of Π_1^0 degrees. This result relies on the construction of a rigid hierarchical structure in a graph model of the hyperbolic plane, and on the fact that every such group admits a representation in PSL_2(ℝ) such that the matrices in the image have coefficients that are computable real numbers.
ER -