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When is a TRAAG orderable?

Yago Antolín, Martín Blufstein, Luis Paris

Abstract

We characterize, in terms of the defining graph, when a twisted right-angled Artin group (a group whose only relations among pairs of generators are either commuting or Klein-bottle type relations) is left-orderable.

When is a TRAAG orderable?

Abstract

We characterize, in terms of the defining graph, when a twisted right-angled Artin group (a group whose only relations among pairs of generators are either commuting or Klein-bottle type relations) is left-orderable.

Paper Structure

This paper contains 5 sections, 8 theorems, 5 equations.

Table of Contents

  1. Introduction
  2. Background
  3. Normal form on TRAAGs
  4. Left-orders on the fundamental group of a Klein bottle
  5. Proofs

Key Result

Theorem 1.5

Let $\Gamma$ be a mixed graph and $G_\Gamma$ be the associated TRAAG. The following holds

Theorems & Definitions (17)

  • Definition 1.1
  • Definition 1.3
  • Remark 1.4
  • Theorem 1.5
  • Theorem 2.1
  • Corollary 2.2
  • proof
  • Lemma 2.4
  • Lemma 2.5
  • Remark 2.6
  • ...and 7 more