Diagram groups are totally orderable
Group Theory
2007-05-23 v1 Geometric Topology
Abstract
In this paper, we introduce the concept of the independence graph of a directed 2-complex. We show that the class of diagram groups is closed under graph products over independence graphs of rooted 2-trees. This allows us to show that a diagram group containing all countable diagram groups is a semi-direct product of a partially commutative group and R. Thompson's group . As a result, we prove that all diagram groups are totally orderable.
Cite
@article{arxiv.math/0305153,
title = {Diagram groups are totally orderable},
author = {Victor Guba and Mark Sapir},
journal= {arXiv preprint arXiv:math/0305153},
year = {2007}
}
Comments
22 pages