Work

A universal algebraic approach to rack coverings

Year: 2025

Type: article

Abstract: We study rack and quandle coverings from a universal algebraic viewpoint. We show how coverings can be understood using the concept of strongly abelian congruences. We provide an abstract characterization of several particular types of covering extensions, such as central and abelian ones. We present a new characterization of simply connected quandles and we show that the categorical notion of normal extension coincides with the notion of central covering. We answer several questions from the papers of Clark, Saito and Vendramin about identities preserved by quandle coverings.

Source: Journal of Knot Theory and Its Ramifications

DOI: 10.1142/s021821652550035x

Authors: Marco Bonatto, David Stanovský

Institutions: Consejo Nacional de Investigaciones Científicas y Técnicas, Universidad de Buenos Aires, Charles University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Grantová Agentura České Republiky

Award: Expanding the Scope of Universal Algebra