Unitary rmatrices, namely unitary solutions to the yangbaxter equation, a. Kassel, turaev, braid groups, graduate texts in mathematics 247, springer. The presentation given here is known as the artin presentation, given. Braid groups graduate texts in mathematics download books. The author also discusses the quantum plane as an object that generalizes the affine plane, namely the two variables x, y generating the plane no longer commute but instead satisfy yx q xy. The conjugacy problem theory and applications jensharlanderbsu,hannahlewisdsc,jonathansiegelucsc,andchaoxusbu the big picture. Thebraidgroup,representations andnonabeliananyons oskar weinberger bachelors thesis sa104x degree project in engineering physics, first cycle department of mathematics kth, royal institute of technology supervisor.
I hope to convey in this talk a feeling of how braid groups work and why they are important. Questions tagged braidgroups mathematics stack exchange. Introduction to braid groups joshua lieber vigre reu 2011 university of chicago abstract. Smoothing each crossing in a diagram produces the seifert circles the seifert number sl is the least sd for any diagram d of l. Thebraidgroup,representations andnonabeliananyons oskar weinberger bachelors thesis sa104x degree project in engineering physics, first cycle. A braid is a certain arrangement of strings in threedimensional space. Let n be an integer greater than or equal to 6 and a surface g. In mathematics, the braid group on n strands, also known as the artin braid group, is the group whose elements are equivalence classes of nbraids, and whose group operation is composition of braids. Read download braid groups graduate texts in mathematics. In mathematics, the braid group on n strands denoted.
Ihara, some details on the gtaction onb n, appendix to. Introduction to braid groups university of chicago. The braid group b n on nstrands is the group with n 1 generators. Braid group representations a thesis presented in partial ful. Braids and braid groups, the focus of this text, have been at the heart of im. Contents 1 introduction 2 2 monodromy representations 11 3 the framed braid. The authors introduce the basic theory of braid groups, highlighting several definitions showing. Bowling ball representations of braid groups journal of. Braid groups by kassel, christian and turaev, vladimir and dodane, o. Braid groups edition 1 by christian kassel, vladimir.
There is an important di erence between the symmetric group s n and the braid group b n. Theorem 3 injectivity of the morphisms from braid groups in the mapping class group. Braid group project gutenberg selfpublishing ebooks. These are the notes of the course \mapping class groups, braid groups and formality held in strasbourg during the second semester of the academic year 20142015 master \math ematiques fondamentales, university of strasbourg. Read braid groups graduatetextsinmathematics online, read in mobile or kindle. Perhaps the longest standing open question concerning the braid groups is whether or not they are linear.
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. Turaev, braid groups, graduate texts in mathematics, vol. Graduate texts in mathematics 247 editorial board s. Example applications of braid groups include knot theory, where any knot may be represented as the closure of certain braids. Introductory lectures on braids, configurations and their applications, world scientific. Braid groups graduate texts in mathematics download. The braid index bl is the least number of strands among all braid. Braid groups graduate texts in mathematics pdf free download.
In this wellwritten presentation, motivated by numerous examples and problems, the authors introduce the basic theory of braid groups, highlighting several definitions that show their equivalence. The automorphism groups of the profinite braid groups. We also prove that, still in the case of the disc, the intersection numbers along straight lines, which conjecturally make sense in in. Introduction in the rst lecture of our tutorial, the knot group of the trefoil was remarked to be the braid group b 3. Sofia lambropoulou international centre for theoretical physics. Braid groups with the graphical assistance of olivier dodane, by christian kassel and vladimir turaev, graduate texts in mathematics, 247. Christian kassel, quantum groups, graduate texts in mathematics, vol.
Braids and braid groups, the focus of this text, have been at the heart of important mathematical developments over the last two decades. Christian kassel, vladimir turaev, braid groups, graduate texts in mathematics 247, springer 2008, isbn 9780387338415 benson farb, dan margalit, a primer on mapping class groups, princeton uni. Its good, but its not the funniest book in the world. Vladimir turaev was also a professor at the cnrs and is currently at indiana university in the department of mathematics. Pdf braid groups graduate texts in mathematics download. Patterns and processes of immigrant labour market insertion in europe routledge research in population and migration. Ribet graduate texts in mathematics 1 takeuti z ari.
This is followed by a treatment of the relationship between braids, knots and links. As central objects in knot theory and 3dimensional. The documentary shows generators and relations to give the artins presentation of the braid group. This book provides an introduction to the theory of quantum groups with emphasis. Patrick dehornoy, braid groups and left distributive operations, transactions ams 345 no. Quantum groups have given many examples of noncommutative noncocommutative bialgebras than were known before this research area had taken off. Turaev, braid groups, gtm 247 springer heidelberg 2008. Inspired by topological quantum computation, we study. The advanced topics cover the burau and the lawrencekrammerbigelow representations of the braid groups, the alexanderconway and jones link polynomials, connections with the representation theory of the iwahorihecke algebras, and the garside structure and orderability of the braid groups.
Braid groups graduatetextsinmathematics also available in docx and mobi. In mathematics, the braid group on n strands, denoted by bn, is a group w. Braid groups graduate texts in mathematics pdf epub. Jun 28, 2008 kassel has numerous publications, including the book quantum groups in the springer gradate texts in mathematics series. Details on these and several other descriptions of the braid groups are carefully provided by kassel and turaevs text braid groups.
Quantum groups kassel pdf preliminaries christian kassel download pdf 1558kb. Download pdf braid groups graduate texts in mathematics. Braid groups christian kassel, vladimir turaev auth. Turaev braid groups, graduate texts in math ematics, 247.
Introduction to representations of braid groups scielo colombia. The alexander and jones polynomials through representations. Important results then look at linearity and orderability. There are, in general, many more connections between knot theory and braid groups. Other generalizations of braids that are not considered in the paper 9 3.
Presentations of generalizations of braids with few generators 9 3. Primary 20f36, 20f10, 20e05, 20f60, 57m25, 57m27, 57r50, 57r52, 20m05. Braids having the same number of strands form a group where the operation is composition, which consists in putting a braid after the other and connecting the strands. Hopf algebras, quantum groups and topological eld theory.
Request pdf on jan 1, 2008, christian kassel and others published braid groups. You may want to pause to check the existence of inverses. First, the concepts of the fundamental group of a topological space, con guration space, and exact sequences are brie. The authors introduce the basic theory of braid groups, highlighting several definitions showing their equivalence. Braids and braid groups have been at the heart of mathematical development over the last two decades. Chapter 2 presents an algorithmic problem, the word problem in braid groups. Braids and braid groups, the focus of this text, have been at the heart of important. Braid groups graduatetextsinmathematics pdf epub download. 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. Braid groups download ebook pdf, epub, tuebl, mobi. Their association with permutations has led to their presence in a number of mathematical fields and physics. Three general classes of representations of braid groups are considered.
He also proved many of the most fundamental results concerning them. In contrast to the symmetric group, the braid group is an in nite group without any nontrivial torsion elements, i. Introduction, historical survey, hopf algebras, basic examples, algebra of regular functions on sl2. The ohio state university 2001 masters examination committee. The theory of braid groups is one of the most fascinating chapters of lowdimensional topology. The advanced topics cover the burau and the lawrencekrammerbigelow representations of the braid groups, the alexanderconway and jones link polynomials, connections with the representation theory of the iwahorihecke algebras, and the garside structure and orderability of the. Braid groups viktoriya ozornova november 7, 2016 braid groups appear in many di. Pdf homology of the braid group with coefficients in the. Braid groups two braids in b n can be \added to yield a new braid by joining the bottom points of the rst braid to the top points of the second. Braid groups were introduced by emil artin in 1925, and by now play a role in various parts of mathematics including knot theory, low dimensional topology, and public key cryptography. Matsumoto, on galois actions on profinite completions of braid groups, in recent developments in the inverse galois. With the graphical assistance of olivier dodane find, read and cite all the research you need on researchgate. Its beauty stems from the attractive geometric nature of braids and from their close relations to other remarkable geometric objects such as knots, links, homeomorphisms of surfaces. Furthermore, the study of these braid groups is also both important to mathematics and applicable to physics.