Polynomial filling functions of sublevel sets in $\mathrm{CAT}(0)$ cube complexes

Weis, Jannis

doi:10.48550/arXiv.2610.06276

§Abstract

We give a criterion ensuring that sufficiently high sublevel sets of a discrete Morse function on a $\mathrm{CAT}(0)$ cube complex have polynomial integral homological filling functions. As one application, we verify this criterion for the Stein–Farley complexes of the Higman–Thompson groups $F_{d,r}$ , $T_{d,r}$ , and $V_{d,r}$ . Consequently, these groups have polynomial homological filling functions in every degree $k\geq2$ .

§Cite this article

BibTeX

@misc{Weis2026Sublevels,
  author = {Weis, Jannis},
  title = {Polynomial filling functions of sublevel sets in $\mathrm{CAT}(0)$ cube complexes},
  year = {2026},
  doi = {10.48550/arXiv.2610.06276},
  eprint = {2610.06276},
  archivePrefix = {arXiv},
  primaryClass = {math.GR},
  note = {Preprint},
  url = {https://arxiv.org/abs/2610.06276}
}

AMSRefs

\bib{Weis2026Sublevels}{article}{
  author={Weis, Jannis},
  title={Polynomial filling functions of sublevel sets in $\mathrm{CAT}(0)$ cube complexes},
  date={2026},
  doi={10.48550/arXiv.2610.06276},
  status={Preprint},
  eprint={arXiv:2610.06276},
  url={https://arxiv.org/abs/2610.06276}
}