On the recognition problem for virtually special cube complexes
Group Theory
2017-06-20 v2 Geometric Topology
Abstract
We address the question of whether the property of being virtually special (in the sense of Haglund and Wise) is algorithmically decidable for finite, non-positively curved cube complexes. Our main theorem shows that it cannot be decided locally, i.e. by examining one hyperplane at a time. Specifically, we prove that there does not exist an algorithm that, given a compact non-positively squared 2-complex X and a hyperplane H in X can decide whether or not there is a finite-sheeted cover of X in which no lift of H self-osculates.
Cite
@article{arxiv.1408.2325,
title = {On the recognition problem for virtually special cube complexes},
author = {Martin R. Bridson and Henry Wilton},
journal= {arXiv preprint arXiv:1408.2325},
year = {2017}
}
Comments
9 pages, 2 figures. This is the final version accepted for publication