Resolutions of CAT(0) cube complexes and accessibility properties
Group Theory
2016-09-21 v1
Abstract
In [4], Dunwoody defined resolutions for finitely presented group actions on simplicial trees, that is, an action of the group on a tree with smaller edge and vertex stabilizers. He, moreover, proved that the size of the resolution is bounded by a constant depending only on the group. Extending Dunwoody's definition of patterns we construct resolutions for group actions on a general finite dimensional CAT(0) cube complex. In dimension two, we bound the number of hyperplanes of this resolution. We apply this result for surfaces and 3-manifolds to bound collections of codimension-1 submanifolds.
Cite
@article{arxiv.1411.0902,
title = {Resolutions of CAT(0) cube complexes and accessibility properties},
author = {Benjamin Beeker and Nir Lazarovich},
journal= {arXiv preprint arXiv:1411.0902},
year = {2016}
}
Comments
17 pages, 10 figures