#### Volume 16, issue 4 (2016)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
Resolutions of CAT(0) cube complexes and accessibility properties

### Benjamin Beeker and Nir Lazarovich

Algebraic & Geometric Topology 16 (2016) 2045–2065
##### Abstract

In 1985, 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. Moreover, he 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.

##### Keywords
geometric group theory, CAT(0) cube complexes, 3–manifolds , actions on trees
Primary: 20E08
Secondary: 20F65