Double Affine Hecke Algebras

Double Affine Hecke Algebras

Author: Ivan Cherednik

Publisher: Cambridge University Press

Published: 2005-03-21

Total Pages: 449

ISBN-13: 0521609186

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This is an essentially self-contained monograph centered on the new double Hecke algebra technique.


Topology '90

Topology '90

Author: Boris N. Apanasov

Publisher: Walter de Gruyter

Published: 2011-10-13

Total Pages: 473

ISBN-13: 3110857723

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This series is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.


On Knots

On Knots

Author: Louis H. Kauffman

Publisher: Princeton University Press

Published: 1987

Total Pages: 500

ISBN-13: 9780691084350

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On Knots is a journey through the theory of knots, starting from the simplest combinatorial ideas--ideas arising from the representation of weaving patterns. From this beginning, topological invariants are constructed directly: first linking numbers, then the Conway polynomial and skein theory. This paves the way for later discussion of the recently discovered Jones and generalized polynomials. The central chapter, Chapter Six, is a miscellany of topics and recreations. Here the reader will find the quaternions and the belt trick, a devilish rope trick, Alhambra mosaics, Fibonacci trees, the topology of DNA, and the author's geometric interpretation of the generalized Jones Polynomial. Then come branched covering spaces, the Alexander polynomial, signature theorems, the work of Casson and Gordon on slice knots, and a chapter on knots and algebraic singularities.The book concludes with an appendix about generalized polynomials.


New Ideas In Low Dimensional Topology

New Ideas In Low Dimensional Topology

Author: Vassily Olegovich Manturov

Publisher: World Scientific

Published: 2015-01-27

Total Pages: 541

ISBN-13: 9814630632

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This book consists of a selection of articles devoted to new ideas and developments in low dimensional topology. Low dimensions refer to dimensions three and four for the topology of manifolds and their submanifolds. Thus we have papers related to both manifolds and to knotted submanifolds of dimension one in three (classical knot theory) and two in four (surfaces in four dimensional spaces). Some of the work involves virtual knot theory where the knots are abstractions of classical knots but can be represented by knots embedded in surfaces. This leads both to new interactions with classical topology and to new interactions with essential combinatorics.


Encyclopedia of Knot Theory

Encyclopedia of Knot Theory

Author: Colin Adams

Publisher: CRC Press

Published: 2021-02-10

Total Pages: 954

ISBN-13: 1000222381

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"Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject." – Ed Witten, Recipient of the Fields Medal "I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It’s a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field." – Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis Knot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications. Many of the articles in this book are accessible to undergraduates who are working on research or taking an advanced undergraduate course in knot theory. More advanced articles will be useful to graduate students working on a related thesis topic, to researchers in another area of topology who are interested in current results in knot theory, and to scientists who study the topology and geometry of biopolymers. Features Provides material that is useful and accessible to undergraduates, postgraduates, and full-time researchers Topics discussed provide an excellent catalyst for students to explore meaningful research and gain confidence and commitment to pursuing advanced degrees Edited and contributed by top researchers in the field of knot theory


Christian-Muslim Relations. A Bibliographical History. Volume 9 Western and Southern Europe (1600-1700)

Christian-Muslim Relations. A Bibliographical History. Volume 9 Western and Southern Europe (1600-1700)

Author:

Publisher: BRILL

Published: 2017-12-05

Total Pages: 1068

ISBN-13: 9004356398

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Christian-Muslim Relations, a Bibliographical History 9 (CMR 9) covering Western and Southern Europe in the period 1600-1700 is a further volume in a general history of relations between the two faiths from the seventh century to the early 20th century. It comprises a series of introductory essays and also the main body of detailed entries which treat all the works, surviving or lost, that have been recorded. These entries provide biographical details of the authors, descriptions and assessments of the works themselves, and complete accounts of manuscripts, editions, translations and studies. The result of collaboration between numerous leading scholars, CMR 9, along with the other volumes in this series is intended as a basic tool for research in Christian-Muslim relations. Section Editors: Clinton Bennett, Luis F. Bernabé Pons, Jaco Beyers, Karoline Cook, Lejla Demiri, Martha Frederiks, David D. Grafton, Stanisław Grodź, Alan Guenther, Emma Loghin, Gordon Nickel, Claire Norton, Reza Pourjavady, Douglas Pratt, Radu Păun, Peter Riddell, Umar Ryad, Mehdi Sajid, Cornelia Soldat, Karel Steenbrink, Davide Tacchini, Ann Thomson, Carsten Walbiner.