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2016 Resolutions of CAT(0) cube complexes and accessibility properties
Benjamin Beeker, Nir Lazarovich
Algebr. Geom. Topol. 16(4): 2045-2065 (2016). DOI: 10.2140/agt.2016.16.2045


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.


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Benjamin Beeker. Nir Lazarovich. "Resolutions of CAT(0) cube complexes and accessibility properties." Algebr. Geom. Topol. 16 (4) 2045 - 2065, 2016.


Received: 26 February 2015; Revised: 11 June 2015; Accepted: 12 September 2015; Published: 2016
First available in Project Euclid: 28 November 2017

zbMATH: 06627568
MathSciNet: MR3546458
Digital Object Identifier: 10.2140/agt.2016.16.2045

Primary: 20E08
Secondary: 20F65

Keywords: 3–manifolds , actions on trees , CAT(0) cube complexes , geometric group theory

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.16 • No. 4 • 2016
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