TY - BOOK ID - 1728206 TI - Braid groups AU - Kassel, Christian AU - Turaev, Vladimir Georgievič AU - Dodane, Olivier PY - 2008 VL - 247 SN - 9780387338415 9780387685489 0387338411 9786611490959 1281490954 0387685480 PB - New York (N.Y.): Springer, DB - UniCat KW - Differential topology KW - Mathematics. KW - Group Theory and Generalizations. KW - Manifolds and Cell Complexes (incl. Diff.Topology). KW - Order, Lattices, Ordered Algebraic Structures. KW - Algebraic Topology. KW - Group theory. KW - Algebra. KW - Algebraic topology. KW - Cell aggregation KW - Mathématiques KW - Groupes, Théorie des KW - Algèbre KW - Topologie algébrique KW - Braid theory KW - Braid theory. KW - Braid. KW - Mathematics KW - Physical Sciences & Mathematics KW - Geometry KW - Théorie des groupes KW - Knot theory. KW - Knots (Topology) KW - Braids, Theory of KW - Theory of braids KW - Ordered algebraic structures. KW - Manifolds (Mathematics). KW - Complex manifolds. KW - Low-dimensional topology KW - Knot theory KW - Topology KW - Mathematical analysis KW - Aggregation, Cell KW - Cell patterning KW - Cell interaction KW - Microbial aggregation KW - Groups, Theory of KW - Substitutions (Mathematics) KW - Algebra KW - Algebraic structures, Ordered KW - Structures, Ordered algebraic KW - Analytic spaces KW - Manifolds (Mathematics) KW - Geometry, Differential UR - https://www.unicat.be/uniCat?func=search&query=sysid:1728206 AB - Braids and braid groups have been at the heart of mathematical development over the last two decades. Braids play an important role in diverse areas of mathematics and theoretical physics. The special beauty of the theory of braids stems from their attractive geometric nature and their close relations to other fundamental geometric objects, such as knots, links, mapping class groups of surfaces, and configuration spaces. In this presentation the authors thoroughly examine various aspects of the theory of braids, starting from basic definitions and then moving to more recent results. The advanced topics cover the Burau and the Lawrence--Krammer--Bigelow representations of the braid groups, the Alexander--Conway and Jones link polynomials, connections with the representation theory of the Iwahori--Hecke algebras, and the Garside structure and orderability of the braid groups. This book will serve graduate students, mathematicians, and theoretical physicists interested in low-dimensional topology and its connections with representation theory. ER -