Braids and Self-Distributivity by Patrick Dehornoy
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.-
Groupoids, Inverse Semigroups, and their Operator Algebras
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Extrinsic Geometry of Foliations
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Progress in Mathematics
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Groups, Radical Rings, and the Yang-Baxter Equation
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Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves
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De Rham Cohomology of Differential Modules on Algebraic Varieties
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Poisson Structures and Their Normal Forms
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Cubic Forms and the Circle Method
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Noncommutative Functional Calculus
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Thermodynamic Formalism and Applications to Dimension Theory
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Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change
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Representation Theory, Mathematical Physics, and Integrable Systems
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Hypoelliptic Laplacian and BottChern Cohomology
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Yamabe-type Equations on Complete, Noncompact Manifolds
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Arithmetic and Geometry Around Galois Theory
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Evolution Equations of Hyperbolic and Schrodinger Type
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Vector Bundles on Complex Projective Spaces
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Residue Currents and Bezout Identities
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Tubes
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Seminaire de Theorie des Nombres, Paris 1987-88
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Lecture Notes on Mean Curvature Flow
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European Congress of Mathematics
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Momentum Maps and Hamiltonian Reduction
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Symplectic Geometry and Secondary Characteristic Classes
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Vanishing Theorems on Complex Manifolds
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Lie Groups: Structure, Actions, and Representations
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Ergodic Theory and Dynamical Systems I
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Andreotti-Grauert Theory by Integral Formulas
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Critical Point Theory for Lagrangian Systems
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Perspectives on Four Decades of Algebraic Geometry, Volume 2
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Complex Approximation
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The Radon Transform
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Quadratic Forms in Infinite Dimensional Vector Spaces
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Arithmetic on Modular Curves
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Complex Kleinian Groups
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Cardinal Invariants on Boolean Algebras
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Discrete Groups in Geometry and Analysis
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Lectures on Functor Homology
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New Horizons in pro-p Groups
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Introduction to Vertex Operator Algebras and Their Representations
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Topological Field Theory, Primitive Forms and Related Topics
"In this book…PDehornoy has accomplished with remarkable success the task of presenting the area of interaction where Artin’s braid groups, left self-distributive systems (LD-systems) and set theory come together in a rigorous and clear manner…The exposition is self-contained and there are no prerequisites. A number of basic results about braid groups, self-distributive algebras, and set theory are provided."
--Mathematical Reviews
| SKU | Unavailable |
| ISBN 13 | 9783034895682 |
| ISBN 10 | 3034895682 |
| Title | Braids and Self-Distributivity |
| Author | Patrick Dehornoy |
| Series | Progress In Mathematics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer Basel |
| Year published | 2012-10-23 |
| Number of pages | 623 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |