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Large profinite genus and extensions in Bestvina-Brady groups

  • Vladimir Vankov
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Abstract

We construct the first examples of uncountable families of residually finite duality groups of type FP, all of which have isomorphic profinite completions, while being pairwise not quasi-isometric. To establish these finiteness properties, we prove conjectures of Leary regarding groups of deck transformations of certain cubical branched covers being residually finite and virtually special. The main new tool is a strong separability result for Bestvina-Brady groups, allowing the extension of any finite quotient of many Bestvina-Brady subgroups to a finite quotient of the whole group. This gives a finite version of the congruence extension property, which we also establish for the same group pairs.

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Cite

BibTeXRIS
BibTeX
@misc{vankov2026large,
  title = {{Large profinite genus and extensions in Bestvina-Brady groups}},
  author = {Vladimir Vankov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32775},
  eprint = {2610.32775},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32775},
}
RIS
TY  - UNPB
TI  - Large profinite genus and extensions in Bestvina-Brady groups
AU  - Vladimir Vankov
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32775
UR  - https://arxiv.org/abs/2610.32775
AB  - We construct the first examples of uncountable families of residually finite duality groups of type FP, all of which have isomorphic profinite completions, while being pairwise not quasi-isometric. To establish these finiteness properties, we prove conjectures of Leary regarding groups of deck transformations of certain cubical branched covers being residually finite and virtually special. The main new tool is a strong separability result for Bestvina-Brady groups, allowing the extension of any finite quotient of many Bestvina-Brady subgroups to a finite quotient of the whole group. This gives a finite version of the congruence extension property, which we also establish for the same group pairs.
ER  -