Titlebook: Braids and Self-Distributivity; Patrick Dehornoy Book 2000 Springer Basel AG 2000 Group theory.Gruppentheorie.Knot theory.algebra.algebrai

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https://doi.org/10.1007/978-3-658-13126-5 aim is to introduce a specific combinatorial technique, called word reversing, which is needed in Chapter III to extend the braid action of Chapter I on LD-systems. The third aim is to develop the techinque of word reversing in a general framework, so as to be able to apply it to a certain group.in Chapter VIII.

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Braids vs. Self-Distributive Systemss based on the concrete idea of colouring the strands of a braid, and left selfdistributivity arises as a natural compatibility condition. At this early stage, some of the constructions may look artificial or strange: it will be one of the aims of the subsequent chapters, in particular in Part B of

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Word Reversing aim is to introduce a specific combinatorial technique, called word reversing, which is needed in Chapter III to extend the braid action of Chapter I on LD-systems. The third aim is to develop the techinque of word reversing in a general framework, so as to be able to apply it to a certain group.in

Insufficient

The Braid Orderarger than 1 are characterized as those braids admitting an expression where the generator with smaller index appears positively only.where some letter . occurs, but the letter σ.does not, nor does any letter σ. with .i. The order is decidable.there exists an effective algorithm that compares any tw

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Normal Formsequivalent. Here, we prove normal form results: we construct several families of distinguished terms such that every term is LD-equivalent to exactly one term in the family. This gives alternative solutions to the word problem, as two terms are LD-equivalent if and only if their normal forms are equ