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Author: Patrick Dehornoy Publisher: American Mathematical Soc. ISBN: 0821844318 Category : Mathematics Languages : en Pages : 339
Book Description
Since the discovery that Artin's braid groups enjoy a left-invariant linear ordering, several different approaches have been used to understand this phenomenon. This text provides an account of those approaches, involving varied objects & domains as combinatorial group theory, self-distributive algebra & finite combinatorics.
Author: Patrick Dehornoy Publisher: American Mathematical Soc. ISBN: 0821844318 Category : Mathematics Languages : en Pages : 339
Book Description
Since the discovery that Artin's braid groups enjoy a left-invariant linear ordering, several different approaches have been used to understand this phenomenon. This text provides an account of those approaches, involving varied objects & domains as combinatorial group theory, self-distributive algebra & finite combinatorics.
Author: A. Jon Berrick Publisher: World Scientific ISBN: 9814291404 Category : Mathematics Languages : en Pages : 414
Book Description
This book is an indispensable guide for anyone seeking to familarize themselves with research in braid groups, configuration spaces and their applications. Starting at the beginning, and assuming only basic topology and group theory, the volume's noted expositors take the reader through the fundamental theory and on to current research and applications in fields as varied as astrophysics, cryptography and robotics. As leading researchers themselves, the authors write enthusiastically about their topics, and include many striking illustrations. The chapters have their origins in tutorials given at a Summer School on Braids, at the National University of Singapore's Institute for Mathematical Sciences in June 2007, to an audience of more than thirty international graduate students.
Author: Patrick Dehornoy Publisher: Birkhäuser ISBN: 3034884427 Category : Mathematics Languages : en Pages : 637
Book Description
This is the award-winning monograph of the Sunyer i Balaguer Prize 1999. The book presents recently discovered connections between Artin’s braid groups and left self-distributive systems, which are sets equipped with a binary operation satisfying the identity x(yz) = (xy)(xz). Although not a comprehensive course, the exposition is self-contained, and many basic results are established. In particular, the first chapters include a thorough algebraic study of Artin’s braid groups.
Author: Adam Clay Publisher: American Mathematical Soc. ISBN: 1470431068 Category : Mathematics Languages : en Pages : 167
Book Description
This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology. The use of topological methods in proving algebraic results is another feature of the book. The book was written to serve both as a textbook for graduate students, containing many exercises, and as a reference for researchers in topology, algebra, and dynamical systems. A basic background in group theory and topology is the only prerequisite for the reader.
Author: Patrick Dehornoy Publisher: Cambridge University Press ISBN: 1108922880 Category : Mathematics Languages : en Pages : 260
Book Description
Everyone knows what braids are, whether they be made of hair, knitting wool, or electrical cables. However, it is not so evident that we can construct a theory about them, i.e. to elaborate a coherent and mathematically interesting corpus of results concerning them. This book demonstrates that there is a resoundingly positive response to this question: braids are fascinating objects, with a variety of rich mathematical properties and potential applications. A special emphasis is placed on the algorithmic aspects and on what can be called the 'calculus of braids', in particular the problem of isotopy. Prerequisites are kept to a minimum, with most results being established from scratch. An appendix at the end of each chapter gives a detailed introduction to the more advanced notions required, including monoids and group presentations. Also included is a range of carefully selected exercises to help the reader test their knowledge, with solutions available.
Author: Louis H. Kauffman Publisher: World Scientific ISBN: 9814313009 Category : Mathematics Languages : en Pages : 577
Book Description
More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book.
Author: Douglas J. LaFountain Publisher: American Mathematical Soc. ISBN: 1470436604 Category : Mathematics Languages : en Pages : 305
Book Description
Offers a self-contained introduction to braid foliation techniques, which is a theory developed to study knots, links and surfaces in general 3-manifolds and more specifically in contact 3-manifolds. With style and content accessible to beginning students interested in geometric topology, each chapter centres around a key theorem or theorems.
Author: John Borrows Publisher: McGill-Queen's Press - MQUP ISBN: 1928096832 Category : Law Languages : en Pages : 256
Book Description
Implementation in Canada of the United Nations Declaration on the Rights of Indigenous Peoples (UNDRIP) is a pivotal opportunity to explore the relationship between international law, Indigenous peoples' own laws, and Canada's constitutional narratives. Two significant statements by the current Liberal government - the May 2016 address by Indigenous Affairs Minister Carolyn Bennett to the Permanent Forum on Indigenous Issues at the United Nations and the September 2017 address to the United Nations by Prime Minister Justin Trudeau - have endorsed UNDRIP and committed Canada to implementing it as “a way forward” on the path to genuine nation-to-nation relationships with Indigenous peoples. In response, these essays engage with the legal, historical, political, and practical aspects of UNDRIP implementation. Written by Indigenous legal scholars and policy leaders, and guided by the metaphor of braiding international, domestic, and Indigenous laws into a strong, unified whole composed of distinct parts, the book makes visible the possibilities for reconciliation from different angles and under different lenses.
Author: Christian Kassel Publisher: Springer Science & Business Media ISBN: 0387685480 Category : Mathematics Languages : en Pages : 349
Book Description
In this well-written presentation, motivated by numerous examples and problems, the authors introduce the basic theory of braid groups, highlighting several definitions that show their equivalence; this is followed by a treatment of the relationship between braids, knots and links. Important results then treat the linearity and orderability of the subject. Relevant additional material is included in five large appendices. Braid Groups will serve graduate students and a number of mathematicians coming from diverse disciplines.
Author: Patrick Dehornoy
Author: Patrick Dehornoy
Author: A. Jon Berrick
Author: Patrick Dehornoy
Author: Adam Clay
Author: Patrick Dehornoy
Author: Louis H. Kauffman
Author: Douglas J. LaFountain
Author: John Borrows
Author: Christian Kassel
Author: Butterick Publishing Company