Quasi-isometry invariance of discrete higher filling functions

Weis, Jannis

doi:10.48550/arXiv.2601.15140

§Abstract

We prove that homological filling functions over a ring $R$ equipped with the discrete norm are quasi-isometry invariants for all groups of type $\mathrm{FP}_n$ . This confirms a conjecture of Bader-Kropholler-Vankov in the case of discrete norms. The proof uses a technique of equipping free chain complexes with a geometric structure, allowing for analogues of cellular constructions in the purely algebraic setting. As a further application we prove quasi-isometry invariance for a weighted version of integral and discrete filling functions originally introduced in the study of the rapid decay property.

§Cite this article

BibTeX

@misc{Weis2026QuasiIsometry,
  author = {Weis, Jannis},
  title = {Quasi-isometry invariance of discrete higher filling functions},
  year = {2026},
  doi = {10.48550/arXiv.2601.15140},
  eprint = {2601.15140},
  archivePrefix = {arXiv},
  primaryClass = {math.GR},
  note = {Preprint},
  url = {https://arxiv.org/abs/2601.15140}
}

AMSRefs

\bib{Weis2026QuasiIsometry}{article}{
  author={Weis, Jannis},
  title={Quasi-isometry invariance of discrete higher filling functions},
  date={2026},
  doi={10.48550/arXiv.2601.15140},
  status={Preprint},
  eprint={arXiv:2601.15140},
  url={https://arxiv.org/abs/2601.15140}
}