Describing all bi-orderings on Thompson's group F
Andr\'es Navas, Crist\'obal Rivas
TL;DR
This paper classifies all bi-orderings on Thompson's group F, revealing a complex structure composed of isolated points and Cantor sets within its space of bi-orderings.
Contribution
It provides a complete description of the space of bi-orderings on Thompson's group F, identifying its topological structure.
Findings
Space of bi-orderings has 8 isolated points.
Contains four canonical copies of the Cantor set.
Complete classification of bi-orderings on F.
Abstract
We describe all possible ways of bi-ordering Thompson group F: its space of bi-orderings is made up of eight isolated points and four canonical copies of the Cantor set.
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Taxonomy
TopicsGeometric and Algebraic Topology · Finite Group Theory Research · semigroups and automata theory