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PreprintCC BY-NC-SA 4.0HAL

Profinite rigidity and quandle colourings

  • Jacques Darné
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Abstract

We show that the numbers of colourings of a link by all finite quandles is equivalent, as an invariant of links, to the profinite completion of the peripheral system. This allows us to reformulate the classical question of the completeness of the former invariant in terms of profinite rigidity. We also develop some profinite quandle theory, and we show that a topological quandle is profinite if and only if it is compact and totally discontinuous and its group of inner automorphism is relatively compact in its homeomorphism group.

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Cite

BibTeXRIS
BibTeX
@misc{darne2026profinite,
  title = {{Profinite rigidity and quandle colourings}},
  author = {Jacques Darné},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06485},
  eprint = {2610.06485},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05776479v1},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Profinite rigidity and quandle colourings
AU  - Jacques Darné
PY  - 2026
DA  - 2026/10/01
PB  - HAL
DO  - 10.48550/arxiv.2610.06485
UR  - https://hal.science/hal-05776479v1
AB  - We show that the numbers of colourings of a link by all finite quandles is equivalent, as an invariant of links, to the profinite completion of the peripheral system. This allows us to reformulate the classical question of the completeness of the former invariant in terms of profinite rigidity. We also develop some profinite quandle theory, and we show that a topological quandle is profinite if and only if it is compact and totally discontinuous and its group of inner automorphism is relatively compact in its homeomorphism group.
ER  -