A continuum of coarse medians for all mapping class groups and right-angled groups

@misc{mangioni2026continuum,
  title = {{A continuum of coarse medians for all mapping class groups and right-angled groups}},
  author = {Giorgio Mangioni},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.09162},
  eprint = {2610.09162},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.09162},
  note = {CC BY-SA 4.0},
}

TY  - UNPB
TI  - A continuum of coarse medians for all mapping class groups and right-angled groups
AU  - Giorgio Mangioni
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.09162
UR  - https://arxiv.org/abs/2610.09162
AB  - It is shown that the mapping class group of any non-sporadic surface admits a continuum of equivariant coarse median structures, thus improving a previous theorem of the author. The same holds for a wide class of right-angled Artin and Coxeter groups, including examples of any dimension at least two, and RACGs which are not quasi-isometric to RAAGs; the coarse median structures in these cases are not induced by cocompact cubulations. The results are instances of a general procedure, which uses quasicocycles to flexibly modify the structure of a (suitable) hierarchically hyperbolic group.
ER  -