PreprintarXiv licencearXiv
From branching quasiflats to flats in CAT(0) cube complexes
Abstract
We study quasiisometric embeddings between finite-dimensional CAT(0) cube complexes. More specifically, we introduce geometric branching conditions under which flats in the domain, not necessarily of top rank, are mapped within finite Hausdorff distance of flats. As a consequence, one obtains embeddings between natural graphs associated with the Tits boundaries of those cube complexes. These results form a key step in understanding quasiisometric embeddings between right-angled Artin groups. In an appendix, we also explain how the same methods recover previously established rigidity results for quasiisometric embeddings of symmetric spaces and Euclidean buildings of the same spherical type.
Related
- Quenched First-Passage Asymptotics for Branching Random Walk on a Hamming Cube
- Polynomial filling functions of sublevel sets in CAT(0) cube complexes
- A weighted inequality for matroid flats and log-concavity of Whitney numbers
- Unavoidable flats in matroids excluding a uniform minor
- Merino-Welsh inequalities for matroids with controlled lattices of cyclic flats
BibTeX
@misc{bader2026from,
title = {{From branching quasiflats to flats in CAT(0) cube complexes}},
author = {Shaked Bader and Oussama Bensaid and Harry Petyt},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.10248},
eprint = {2605.10248},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.10248},
}
RIS
TY - UNPB
TI - From branching quasiflats to flats in CAT(0) cube complexes
AU - Shaked Bader
AU - Oussama Bensaid
AU - Harry Petyt
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2605.10248
UR - https://arxiv.org/abs/2605.10248
AB - We study quasiisometric embeddings between finite-dimensional CAT(0) cube complexes. More specifically, we introduce geometric branching conditions under which flats in the domain, not necessarily of top rank, are mapped within finite Hausdorff distance of flats. As a consequence, one obtains embeddings between natural graphs associated with the Tits boundaries of those cube complexes. These results form a key step in understanding quasiisometric embeddings between right-angled Artin groups. In an appendix, we also explain how the same methods recover previously established rigidity results for quasiisometric embeddings of symmetric spaces and Euclidean buildings of the same spherical type.
ER -