Garside and quadratic normalisation: a survey
Patrick Dehornoy
TL;DR
This survey explores Garside and quadratic normalisation methods in monoids, detailing their mechanisms, extensions, and characterisations, providing a comprehensive overview of their theoretical framework and applications.
Contribution
It offers a detailed analysis of Garside normalisation, extends the understanding to quadratic procedures, and characterises Garside normalisation within this broader context.
Findings
Garside normalisation mechanism is thoroughly analyzed.
Quadratic normalisation procedures are characterized and compared.
Garside normalisation is identified among quadratic procedures.
Abstract
Starting from the seminal example of the greedy normal norm in braid monoids, we analyse the mechanism of the normal form in a Garside monoid and explain how it extends to the more general framework of Garside families. Extending the viewpoint even more, we then consider general quadratic normalisation procedures and characterise Garside normalisation among them.
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Taxonomy
Topicssemigroups and automata theory · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology