English

Cleanliness versus Specialness

Group Theory 2025-03-24 v1

Abstract

We show that the fundamental group of a geometrically clean graph of finite rank free groups does not need to be virtually compact special, answering a question of Wise. This implies that the class of the virtually VH-clean graphs of finite rank free groups is a proper subclass of the class of virtually geometrically clean graphs of finite rank free groups.

Keywords

Cite

@article{arxiv.2503.16722,
  title  = {Cleanliness versus Specialness},
  author = {Kasia Jankiewicz},
  journal= {arXiv preprint arXiv:2503.16722},
  year   = {2025}
}

Comments

6 pages, 4 figures. Comments are welcome!

R2 v1 2026-06-28T22:29:05.289Z