Circular orderability and quandles
Idrissa Ba, Mohamed Elhamdadi
TL;DR
This paper introduces the concept of circular orderability for quandles, explores the topological structure of their orderings, and provides examples of quandles with specific orderability properties.
Contribution
It defines circular orderability for quandles, analyzes the topological space of their orderings, and presents examples illustrating various orderability cases.
Findings
The set of all circular orderings of a quandle is a compact topological space.
The space of quandle orderings embeds into the space of circular orderings.
Examples of quandles not circularly orderable are provided.
Abstract
In this paper, we introduce the notion of circular orderability for quandles. We show that the set all right (respectively left) circular orderings of a quandle is a compact topological space. We also show that the space of right (respectively left) orderings of a quandle embeds in its space of right (respectively left) circular orderings. Examples of quandles that are not left circularly orderable and examples of quandles that are neither left nor right circularly orderable are given.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topology and Set Theory · Mathematical and Theoretical Analysis · Rings, Modules, and Algebras