Geodesic
Resolutions of CAT(0) cube complexes and accessibility properties
Beeker, Benjamin1 ; Lazarovich, Nir2
1Department of Mathematics, Hebrew University, 9190401 Jerusalem, Israel
2Department of Mathematics, ETH Zürich, Rämistrasse 101, CH-8092 Zürich, Switzerland
Algebraic and Geometric Topology, Tome 16 (2016) no. 4, pp. 2045-2065
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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.

DOI : 10.2140/agt.2016.16.2045
Classification : 20E08, 20F65
Keywords: geometric group theory, CAT(0) cube complexes, 3–manifolds , actions on trees

Beeker, Benjamin  1   ; Lazarovich, Nir  2

1 Department of Mathematics, Hebrew University, 9190401 Jerusalem, Israel
2 Department of Mathematics, ETH Zürich, Rämistrasse 101, CH-8092 Zürich, Switzerland 
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Beeker, Benjamin; Lazarovich, Nir. Resolutions of CAT(0) cube complexes and accessibility properties. Algebraic and Geometric Topology, Tome 16 (2016) no. 4, pp. 2045-2065. doi: 10.2140/agt.2016.16.2045

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