## Ordering Braids (Mathematical Surveys and Monographs) by Patrick Dehornoy

By Patrick Dehornoy

Within the fifteen years because the discovery that Artin's braid teams take pleasure in a left-invariant linear ordering, a number of really diverse techniques were used to appreciate this phenomenon. This e-book is an account of these methods, which contain such assorted items and domain names as combinatorial staff conception, self-distributive algebra, finite combinatorics, automata, low-dimensional topology, mapping category teams, and hyperbolic geometry. The impressive element is that each one those ways bring about an identical ordering, making the latter relatively canonical. we've got tried to make the guidelines during this quantity obtainable and engaging to scholars and professional pros alike. even if the textual content touches upon many various components, we purely think that the reader has a few easy historical past in staff thought and topology, and we contain distinctive introductions anywhere they are wanted, with a view to make the booklet as self-contained as attainable. the current quantity follows the e-book, Why are braids orderable?, written via an identical authors and released in 2002 by means of the Societe Mathematique de France. the present textual content includes a huge volume of latest fabric, together with principles that have been unknown in 2002. furthermore, a lot of the unique textual content has been thoroughly rewritten, for you to making it extra readable and updated.