Knots Groups And 3 Manifolds

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Knots, Groups and 3-Manifolds (AM-84), Volume 84

Author : Lee Paul Neuwirth
Publisher : Princeton University Press
ISBN 13 : 140088151X
Total Pages : 346 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Knots, Groups and 3-Manifolds (AM-84), Volume 84 by : Lee Paul Neuwirth

Download or read book Knots, Groups and 3-Manifolds (AM-84), Volume 84 written by Lee Paul Neuwirth and published by Princeton University Press. This book was released on 2016-03-02 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is a sympathy of ideas among the fields of knot theory, infinite discrete group theory, and the topology of 3-manifolds. This book contains fifteen papers in which new results are proved in all three of these fields. These papers are dedicated to the memory of Ralph H. Fox, one of the world's leading topologists, by colleagues, former students, and friends. In knot theory, papers have been contributed by Goldsmith, Levine, Lomonaco, Perko, Trotter, and Whitten. Of these several are devoted to the study of branched covering spaces over knots and links, while others utilize the braid groups of Artin. Cossey and Smythe, Stallings, and Strasser address themselves to group theory. In his contribution Stallings describes the calculation of the groups In/In+1 where I is the augmentation ideal in a group ring RG. As a consequence, one has for each k an example of a k-generator l-relator group with no free homomorphs. In the third part, papers by Birman, Cappell, Milnor, Montesinos, Papakyriakopoulos, and Shalen comprise the treatment of 3-manifolds. Milnor gives, besides important new results, an exposition of certain aspects of our current knowledge regarding the 3- dimensional Brieskorn manifolds.

Quantum Invariants of Knots and 3-Manifolds

Author : Vladimir G. Turaev
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110435225
Total Pages : 608 pages
Book Rating : 4.1/5 (14 download)

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Book Synopsis Quantum Invariants of Knots and 3-Manifolds by : Vladimir G. Turaev

Download or read book Quantum Invariants of Knots and 3-Manifolds written by Vladimir G. Turaev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-07-11 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to the strong appeal and wide use of this monograph, it is now available in its third revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups. The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space. This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. Contents: Invariants of graphs in Euclidean 3-space and of closed 3-manifolds Foundations of topological quantum field theory Three-dimensional topological quantum field theory Two-dimensional modular functors 6j-symbols Simplicial state sums on 3-manifolds Shadows of manifolds and state sums on shadows Constructions of modular categories

Knots, Links, Braids and 3-Manifolds

Author : Viktor Vasilʹevich Prasolov
Publisher : American Mathematical Soc.
ISBN 13 : 0821808982
Total Pages : 250 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Knots, Links, Braids and 3-Manifolds by : Viktor Vasilʹevich Prasolov

Download or read book Knots, Links, Braids and 3-Manifolds written by Viktor Vasilʹevich Prasolov and published by American Mathematical Soc.. This book was released on 1997 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the remarkable work of Vaughan Jones and Victor Vassiliev on knot and link invariants and its recent modifications and generalizations, including a mathematical treatment of Jones-Witten invariants. The mathematical prerequisites are minimal compared to other monographs in this area. Numerous figures and problems make this book suitable as a graduate level course text or for self-study.

Introduction to 3-Manifolds

Author : Jennifer Schultens
Publisher : American Mathematical Soc.
ISBN 13 : 1470410206
Total Pages : 298 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Introduction to 3-Manifolds by : Jennifer Schultens

Download or read book Introduction to 3-Manifolds written by Jennifer Schultens and published by American Mathematical Soc.. This book was released on 2014-05-21 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of a graduate course on 3-manifolds and is intended for a mathematically experienced audience that is new to low-dimensional topology. The exposition begins with the definition of a manifold, explores possible additional structures on manifolds, discusses the classification of surfaces, introduces key foundational results for 3-manifolds, and provides an overview of knot theory. It then continues with more specialized topics by briefly considering triangulations of 3-manifolds, normal surface theory, and Heegaard splittings. The book finishes with a discussion of topics relevant to viewing 3-manifolds via the curve complex. With about 250 figures and more than 200 exercises, this book can serve as an excellent overview and starting point for the study of 3-manifolds.

Knots and Links

Author : Dale Rolfsen
Publisher : American Mathematical Soc.
ISBN 13 : 0821834363
Total Pages : 458 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Knots and Links by : Dale Rolfsen

Download or read book Knots and Links written by Dale Rolfsen and published by American Mathematical Soc.. This book was released on 2003 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds. Besides providing a guide to understanding knot theory, the book offers 'practical' training. After reading it, you will be able to do many things: compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements.It is characterized by its hands-on approach and emphasis on a visual, geometric understanding. Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included. Now back in print by the AMS, the book is still a standard reference in knot theory. It is written in a remarkable style that makes it useful for both beginners and researchers. Particularly noteworthy is the table of knots and links at the end. This volume is an excellent introduction to the topic and is suitable as a textbook for a course in knot theory or 3-manifolds. Other key books of interest on this topic available from the AMS are ""The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes"" and ""The Knot Book.""

Knot Groups

Author : Lee Paul Neuwirth
Publisher : Princeton University Press
ISBN 13 : 0691079919
Total Pages : 119 pages
Book Rating : 4.6/5 (91 download)

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Book Synopsis Knot Groups by : Lee Paul Neuwirth

Download or read book Knot Groups written by Lee Paul Neuwirth and published by Princeton University Press. This book was released on 1965-03-21 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Knot Groups. Annals of Mathematics Studies. (AM-56), Volume 56, will be forthcoming.

Knots, Groups, and 3-manifolds

Author : L. P. Neuwirth
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (11 download)

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Book Synopsis Knots, Groups, and 3-manifolds by : L. P. Neuwirth

Download or read book Knots, Groups, and 3-manifolds written by L. P. Neuwirth and published by . This book was released on 1975 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Knots, Groups, and 3-manifolds

Author : Lee Paul Neuwirth
Publisher :
ISBN 13 :
Total Pages : 337 pages
Book Rating : 4.:/5 (163 download)

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Book Synopsis Knots, Groups, and 3-manifolds by : Lee Paul Neuwirth

Download or read book Knots, Groups, and 3-manifolds written by Lee Paul Neuwirth and published by . This book was released on 1975 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt:

3-manifold Groups

Author : Matthias Aschenbrenner
Publisher : Erich Schmidt Verlag GmbH & Co. KG
ISBN 13 : 9783037191545
Total Pages : 236 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis 3-manifold Groups by : Matthias Aschenbrenner

Download or read book 3-manifold Groups written by Matthias Aschenbrenner and published by Erich Schmidt Verlag GmbH & Co. KG. This book was released on 2015 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of 3-manifold topology has made great strides forward since 1982 when Thurston articulated his influential list of questions. Primary among these is Perelman's proof of the Geometrization Conjecture, but other highlights include the Tameness Theorem of Agol and Calegari-Gabai, the Surface Subgroup Theorem of Kahn-Markovic, the work of Wise and others on special cube complexes, and, finally, Agol's proof of the Virtual Haken Conjecture. This book summarizes all these developments and provides an exhaustive account of the current state of the art of 3-manifold topology, especially focusing on the consequences for fundamental groups of 3-manifolds. As the first book on 3-manifold topology that incorporates the exciting progress of the last two decades, it will be an invaluable resource for researchers in the field who need a reference for these developments. It also gives a fast-paced introduction to this material. Although some familiarity with the fundamental group is recommended, little other previous knowledge is assumed, and the book is accessible to graduate students. The book closes with an extensive list of open questions which will also be of interest to graduate students and established researchers.

Quantum Invariants

Author : Tomotada Ohtsuki
Publisher : World Scientific
ISBN 13 : 9789812811172
Total Pages : 516 pages
Book Rating : 4.8/5 (111 download)

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Book Synopsis Quantum Invariants by : Tomotada Ohtsuki

Download or read book Quantum Invariants written by Tomotada Ohtsuki and published by World Scientific. This book was released on 2002 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The ChernOCoSimons field theory and the WessOCoZuminoOCoWitten model are described as the physical background of the invariants. Contents: Knots and Polynomial Invariants; Braids and Representations of the Braid Groups; Operator Invariants of Tangles via Sliced Diagrams; Ribbon Hopf Algebras and Invariants of Links; Monodromy Representations of the Braid Groups Derived from the KnizhnikOCoZamolodchikov Equation; The Kontsevich Invariant; Vassiliev Invariants; Quantum Invariants of 3-Manifolds; Perturbative Invariants of Knots and 3-Manifolds; The LMO Invariant; Finite Type Invariants of Integral Homology 3-Spheres. Readership: Researchers, lecturers and graduate students in geometry, topology and mathematical physics."

Knots and Primes

Author : Masanori Morishita
Publisher : Springer Nature
ISBN 13 : 9819992559
Total Pages : 268 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis Knots and Primes by : Masanori Morishita

Download or read book Knots and Primes written by Masanori Morishita and published by Springer Nature. This book was released on with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures on the Topology of 3-manifolds

Author : Nikolai Saveliev
Publisher : Walter de Gruyter
ISBN 13 : 9783110162721
Total Pages : 220 pages
Book Rating : 4.1/5 (627 download)

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Book Synopsis Lectures on the Topology of 3-manifolds by : Nikolai Saveliev

Download or read book Lectures on the Topology of 3-manifolds written by Nikolai Saveliev and published by Walter de Gruyter. This book was released on 1999 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:

2-Knots and Their Groups

Author : Jonathan Hillman
Publisher : CUP Archive
ISBN 13 : 9780521378123
Total Pages : 180 pages
Book Rating : 4.3/5 (781 download)

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Book Synopsis 2-Knots and Their Groups by : Jonathan Hillman

Download or read book 2-Knots and Their Groups written by Jonathan Hillman and published by CUP Archive. This book was released on 1989-03-30 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: To attack certain problems in 4-dimensional knot theory the author draws on a variety of techniques, focusing on knots in S^T4, whose fundamental groups contain abelian normal subgroups. Their class contains the most geometrically appealing and best understood examples. Moreover, it is possible to apply work in algebraic methods to these problems. Work in four-dimensional topology is applied in later chapters to the problem of classifying 2-knots.

Torsions of 3-dimensional Manifolds

Author : Vladimir Turaev
Publisher : Birkhäuser
ISBN 13 : 3034879997
Total Pages : 201 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Torsions of 3-dimensional Manifolds by : Vladimir Turaev

Download or read book Torsions of 3-dimensional Manifolds written by Vladimir Turaev and published by Birkhäuser. This book was released on 2012-12-06 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This is an excellent exposition about abelian Reidemeister torsions for three-manifolds." —Zentralblatt Math "This monograph contains a wealth of information many topologists will find very handy. ...Many of the new points of view pioneered by Turaev are gradually becoming mainstream and are spreading beyond the pure topology world. This monograph is a timely and very useful addition to the scientific literature." —Mathematical Reviews

A Survey of Knot Theory

Author : Akio Kawauchi
Publisher : Birkhäuser
ISBN 13 : 3034892276
Total Pages : 431 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis A Survey of Knot Theory by : Akio Kawauchi

Download or read book A Survey of Knot Theory written by Akio Kawauchi and published by Birkhäuser. This book was released on 2012-12-06 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory.

Representing 3-manifolds By Filling Dehn Surfaces

Author : Ruben Vigara Benito
Publisher : World Scientific
ISBN 13 : 9814725501
Total Pages : 299 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Representing 3-manifolds By Filling Dehn Surfaces by : Ruben Vigara Benito

Download or read book Representing 3-manifolds By Filling Dehn Surfaces written by Ruben Vigara Benito and published by World Scientific. This book was released on 2016-03-11 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the beautiful and deep subject of filling Dehn surfaces in the study of topological 3-manifolds. This book presents, for the first time in English and with all the details, the results from the PhD thesis of the first author, together with some more recent results in the subject. It also presents some key ideas on how these techniques could be used on other subjects.Representing 3-Manifolds by Filling Dehn Surfaces is mostly self-contained requiring only basic knowledge on topology and homotopy theory. The complete and detailed proofs are illustrated with a set of more than 600 spectacular pictures, in the tradition of low-dimensional topology books. It is a basic reference for researchers in the area, but it can also be used as an advanced textbook for graduate students or even for adventurous undergraduates in mathematics. The book uses topological and combinatorial tools developed throughout the twentieth century making the volume a trip along the history of low-dimensional topology.

The Geometry and Topology of Three-Manifolds

Author : William P. Thurston
Publisher : American Mathematical Society
ISBN 13 : 1470474743
Total Pages : 337 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Geometry and Topology of Three-Manifolds by : William P. Thurston

Download or read book The Geometry and Topology of Three-Manifolds written by William P. Thurston and published by American Mathematical Society. This book was released on 2023-06-16 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I–III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff. Volume IV contains Thurston's highly influential, though previously unpublished, 1977–78 Princeton Course Notes on the Geometry and Topology of 3-manifolds. It is an indispensable part of the Thurston collection but can also be used on its own as a textbook or for self-study.