Ordered bases, order-preserving automorphisms and bi-orderable link groups

TL;DR

This paper introduces a new criterion for bi-ordering free groups invariant under automorphisms and applies it to prove the bi-orderability of the fundamental group of the magic manifold, addressing a specific open question.

Contribution

It provides a novel criterion for bi-orderings in free groups and demonstrates its application to a significant topological group, the magic manifold's fundamental group.

Findings

Bi-ordering criterion for free groups under automorphisms

Proof that the magic manifold's fundamental group is bi-orderable

Addresses an open question by Kin and Rolfsen

Abstract

We give a new criterion which guarantees that a free group admits a bi-ordering that is invariant under a given automorphism. As an application, we show that the fundamental group of the "magic manifold" is bi-orderable, answering a question of Kin and Rolfsen.