Length functions of 2-dimensional right-angled Artin groups
Ruth Charney, Max Margolis
TL;DR
This paper extends the understanding of length functions from free groups to 2-dimensional right-angled Artin groups acting on CAT(0) rectangle complexes, establishing a similar determination principle.
Contribution
It proves an analogue of Morgan and Culler's theorem for 2-dimensional right-angled Artin groups acting on CAT(0) rectangle complexes.
Findings
Minimal actions are determined by length functions
Extension of length function theory to 2D right-angled Artin groups
New characterization of group actions on CAT(0) rectangle complexes
Abstract
Morgan and Culler proved that a minimal action of a free group on a tree is determined by its translation length function. We prove an analogue of this theorem for 2-dimensional right-angled Artin groups acting on CAT(0) rectangle complexes.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models