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PreprintarXiv licencearXiv

Conjugator length of Bestvina-Brady groups

  • Jerónimo García-Mejía
  • Matteo Migliorini
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Abstract

We classify the conjugator length functions of Bestvina-Brady groups. We show that the conjugator length function, when non-trivial, grows as a linear or quadratic polynomial. In fact, we give explicit criteria on the defining graph to determine the precise degree of the polynomial. The proof generalises ideas of Bridson, Riley, and Sale by exploiting the framework developed by Chang and the authors to classify the Dehn functions of Bestvina-Brady groups.

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Cite

BibTeXRIS
BibTeX
@misc{garciamejia2026conjugator,
  title = {{Conjugator length of Bestvina-Brady groups}},
  author = {Jerónimo García-Mejía and Matteo Migliorini},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.05619},
  eprint = {2611.05619},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.05619},
}
RIS
TY  - UNPB
TI  - Conjugator length of Bestvina-Brady groups
AU  - Jerónimo García-Mejía
AU  - Matteo Migliorini
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.05619
UR  - https://arxiv.org/abs/2611.05619
AB  - We classify the conjugator length functions of Bestvina-Brady groups. We show that the conjugator length function, when non-trivial, grows as a linear or quadratic polynomial. In fact, we give explicit criteria on the defining graph to determine the precise degree of the polynomial. The proof generalises ideas of Bridson, Riley, and Sale by exploiting the framework developed by Chang and the authors to classify the Dehn functions of Bestvina-Brady groups.
ER  -