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Cover: 9783764363437 | Braids and Self-Distributivity | Patrick Dehornoy | Buch | xix | 2000
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Braids and Self-Distributivity
Buch von Patrick Dehornoy
Sprache: Englisch

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Beschreibung
The aim of this book is to present recently discovered connections between Artin's braid groups En and left self-distributive systems (also called LD­ systems), which are sets equipped with a binary operation satisfying the left self-distributivity identity x(yz) = (xy)(xz). (LD) Such connections appeared in set theory in the 1980s and led to the discovery in 1991 of a left invariant linear order on the braid groups. Braids and self-distributivity have been studied for a long time. Braid groups were introduced in the 1930s by E. Artin, and they have played an increas­ ing role in mathematics in view of their connection with many fields, such as knot theory, algebraic combinatorics, quantum groups and the Yang-Baxter equation, etc. LD-systems have also been considered for several decades: early examples are mentioned in the beginning of the 20th century, and the first general results can be traced back to Belousov in the 1960s. The existence of a connection between braids and left self-distributivity has been observed and used in low dimensional topology for more than twenty years, in particular in work by Joyce, Brieskorn, Kauffman and their students. Brieskorn mentions that the connection is already implicit in (Hurwitz 1891). The results we shall concentrate on here rely on a new approach developed in the late 1980s and originating from set theory.
The aim of this book is to present recently discovered connections between Artin's braid groups En and left self-distributive systems (also called LD­ systems), which are sets equipped with a binary operation satisfying the left self-distributivity identity x(yz) = (xy)(xz). (LD) Such connections appeared in set theory in the 1980s and led to the discovery in 1991 of a left invariant linear order on the braid groups. Braids and self-distributivity have been studied for a long time. Braid groups were introduced in the 1930s by E. Artin, and they have played an increas­ ing role in mathematics in view of their connection with many fields, such as knot theory, algebraic combinatorics, quantum groups and the Yang-Baxter equation, etc. LD-systems have also been considered for several decades: early examples are mentioned in the beginning of the 20th century, and the first general results can be traced back to Belousov in the 1960s. The existence of a connection between braids and left self-distributivity has been observed and used in low dimensional topology for more than twenty years, in particular in work by Joyce, Brieskorn, Kauffman and their students. Brieskorn mentions that the connection is already implicit in (Hurwitz 1891). The results we shall concentrate on here rely on a new approach developed in the late 1980s and originating from set theory.
Inhaltsverzeichnis
A: Ordering the Braids.- I. Braids vs. Self-Distributive Systems.- II. Word Reversing.- III. The Braid Order.- IV. The Order on Positive Braids.- B: Free LD-systems.- V. Orders on Free LD-systems.- VI. Normal Forms.- VII. The Geometry Monoid.- VIII. The Group of Left Self-Distributivity.- IX. Progressive Expansions.- C: Other LD-Systems.- X. More LD-Systems.- XI. LD-Monoids.- XII. Elementary Embeddings.- XIII. More about the Laver Tables.- List of Symbols.
Details
Erscheinungsjahr: 2000
Fachbereich: Allgemeines
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Thema: Lexika
Medium: Buch
Reihe: Progress in Mathematics
Inhalt: xix
623 S.
ISBN-13: 9783764363437
ISBN-10: 3764363436
Sprache: Englisch
Herstellernummer: 10768723
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Dehornoy, Patrick
Hersteller: Birkhäuser Basel
Springer Basel AG
Progress in Mathematics
Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße: 241 x 160 x 40 mm
Von/Mit: Patrick Dehornoy
Erscheinungsdatum: 01.07.2000
Gewicht: 1,133 kg
Artikel-ID: 101955627
Inhaltsverzeichnis
A: Ordering the Braids.- I. Braids vs. Self-Distributive Systems.- II. Word Reversing.- III. The Braid Order.- IV. The Order on Positive Braids.- B: Free LD-systems.- V. Orders on Free LD-systems.- VI. Normal Forms.- VII. The Geometry Monoid.- VIII. The Group of Left Self-Distributivity.- IX. Progressive Expansions.- C: Other LD-Systems.- X. More LD-Systems.- XI. LD-Monoids.- XII. Elementary Embeddings.- XIII. More about the Laver Tables.- List of Symbols.
Details
Erscheinungsjahr: 2000
Fachbereich: Allgemeines
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Thema: Lexika
Medium: Buch
Reihe: Progress in Mathematics
Inhalt: xix
623 S.
ISBN-13: 9783764363437
ISBN-10: 3764363436
Sprache: Englisch
Herstellernummer: 10768723
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Dehornoy, Patrick
Hersteller: Birkhäuser Basel
Springer Basel AG
Progress in Mathematics
Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße: 241 x 160 x 40 mm
Von/Mit: Patrick Dehornoy
Erscheinungsdatum: 01.07.2000
Gewicht: 1,133 kg
Artikel-ID: 101955627
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