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arXiv · 1411.0902

Resolutions of CAT(0) cube complexes and accessibility properties

Benjamin Beeker·Nir Lazarovich
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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.

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Benjamin Beeker, Nir Lazarovich. 2014-11-04. Resolutions of CAT(0) cube complexes and accessibility properties. https://doi.org/10.2140/agt.2016.16.2045

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