Cleanliness versus Specialness
arXiv:2503.16722
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.
6 pages, 4 figures. Comments are welcome!