PreprintarXiv licencearXiv
LInearity of Tubular Groups
Abstract
We prove that a tubular group is linear if and only if it is residually finite, equivalently virtually primitive. Every such group embeds in SLn(Z[u]). For a primitive tubular decomposition with at most m edge slopes at each vertex, our representation has dimension 2max{2,m}. In particular, Gersten's group embeds in SL6(Z[u]), and this dimension is minimal.
Related
- Linearity of Graph Manifold Groups
- Commensurability and quasi-isometry classification for one vertex one loop tubular groups
- The Quasi-linearity problem for Jordan-Banach algebras: a topological characterization
- Relative Rouquier linearity and inverse hybrid Kazhdan-Lusztig positivity
- The linearity Conjecture
BibTeX
@misc{wise2026linearity,
title = {{LInearity of Tubular Groups}},
author = {Daniel T. Wise},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12590},
eprint = {2610.12590},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12590},
}
RIS
TY - UNPB
TI - LInearity of Tubular Groups
AU - Daniel T. Wise
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12590
UR - https://arxiv.org/abs/2610.12590
AB - We prove that a tubular group is linear if and only if it is residually finite, equivalently virtually primitive. Every such group embeds in SL_n(Z[u]). For a primitive tubular decomposition with at most m edge slopes at each vertex, our representation has dimension 2max{2,m}. In particular, Gersten's group embeds in SL_6(Z[u]), and this dimension is minimal.
ER -