A Brown Theorem for Dehn functions of graphs of groups

Llosa Isenrich, Claudio; Weis, Jannis

doi:10.48550/arXiv.2608.07191

§Abstract

We prove an upper bound on the Dehn function of a group $G$ acting cellularly, cocompactly, and without inversions on a simply connected CW complex $X$ in terms of the Dehn functions of the vertex stabilizers, the Dehn function of $X$ , and the distortion of the edge stabilizers, provided that $X$ is either a tree or the stabilizer of each $2$ -cell has finite index in the stabilizer of every edge in its boundary. This provides a Dehn function analogue of Brown's Theorem for finiteness properties and an answer to a question of Zaremsky in these cases. We also prove analogues of our result for higher Dehn functions when $X$ is a tree.

§Cite this article

BibTeX

@misc{LlosaIsenrichWeis2026,
  author = {Llosa Isenrich, Claudio and Weis, Jannis},
  title = {A {Brown} Theorem for {Dehn} functions of graphs of groups},
  year = {2026},
  doi = {10.48550/arXiv.2608.07191},
  eprint = {2608.07191},
  archivePrefix = {arXiv},
  primaryClass = {math.GR},
  note = {Preprint},
  url = {https://arxiv.org/abs/2608.07191}
}

AMSRefs

\bib{LlosaIsenrichWeis2026}{article}{
  author={Llosa Isenrich, Claudio},
  author={Weis, Jannis},
  title={A {Brown} Theorem for {Dehn} functions of graphs of groups},
  date={2026},
  doi={10.48550/arXiv.2608.07191},
  status={Preprint},
  eprint={arXiv:2608.07191},
  url={https://arxiv.org/abs/2608.07191}
}