Continuous graph homomorphisms of higher dimensional abelian group actions

@misc{wang2026continuous,
  title = {{Continuous graph homomorphisms of higher dimensional abelian group actions}},
  author = {Ruijun Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39824},
  eprint = {2609.39824},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39824},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Continuous graph homomorphisms of higher dimensional abelian group actions
AU  - Ruijun Wang
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39824
UR  - https://arxiv.org/abs/2609.39824
AB  - For every fixed integer d≥2, we prove that the finite graphs receiving a continuous homomorphism from the standard Schreier graph F(2^ℤ^d) form a Σ^0_1-complete set. This extends a theorem of Gao, Jackson, Krohne and Seward when d=2. For the positive part of the reduction, we show that if a graph H satisfies a certain property then there is a continuous graph homomorphism from F(2^ℤ^d) to H, in particular, the complete graph K_4 satisfies this property. This extends a theorem of Gao and Jackson. We also prove that (ℋ_d ) is a strictly decreasing sequence.
ER  -