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PreprintCC BY 4.0arXiv

Compact Quantum Metric Spaces from Weakly Geodesic Length Functions on Hyperbolic Groups

  • Are Austad
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Abstract

We show that length functions on hyperbolic groups whose induced metrics are hyperbolic and weakly geodesic naturally give rise to compact quantum metric spaces, thus generalizing the result of Ozawa and Rieffel. As a result we obtain several new examples of compact quantum metric spaces, in particular arising from Green metrics associated with random walks on hyperbolic groups, and from proper cocompact isometric actions on proper geodesic hyperbolic spaces admitting a point with trivial stabilizer.

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Cite

BibTeXRIS
BibTeX
@misc{austad2026compact,
  title = {{Compact Quantum Metric Spaces from Weakly Geodesic Length Functions on Hyperbolic Groups}},
  author = {Are Austad},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.28303},
  eprint = {2608.28303},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.28303},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Compact Quantum Metric Spaces from Weakly Geodesic Length Functions on Hyperbolic Groups
AU  - Are Austad
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.28303
UR  - https://arxiv.org/abs/2608.28303
AB  - We show that length functions on hyperbolic groups whose induced metrics are hyperbolic and weakly geodesic naturally give rise to compact quantum metric spaces, thus generalizing the result of Ozawa and Rieffel. As a result we obtain several new examples of compact quantum metric spaces, in particular arising from Green metrics associated with random walks on hyperbolic groups, and from proper cocompact isometric actions on proper geodesic hyperbolic spaces admitting a point with trivial stabilizer.
ER  -