New York: W. H. Freeman and Company, 1994. — 306 p. — ISBN10: 071672393X; ISBN13: 978-0716723936. If you are a student of mathematics, a scientist working in fields affected by knot theory research, or a curious amateur who finds mathematics intriguing, The Knot Book is for you. With this engagingly written and illustrated book, you will be working with some of the most...
W.H. Freeman and Company, 2004. — 306 p. — ISBN: 978-0-8218-3678-1. Knots are familiar objects. We use them to moor our boats, to wrap our packages, to tie our shoes. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. The Knot Book is an introduction to this rich theory, starting with our familiar understanding of knots and a bit of...
New York: W. H. Freeman and Company, 1994. — 306 p. — ISBN13: 978-0716723936. Over a century old, knot theory is today one of the most active areas of modern mathematics. The study of knots has led to important applications in DNA research and the synthesis of new molecules, and has had a significant impact on statistical mechanics and quantum field theory. Colin Adams’s The...
American Mathematical Society, 2004. — 307 p. — ISBN: 0-8218-3678-1. Knots are familiar objects. We use them to moor our boats, to wrap our packages, to tie our shoes. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. "The Knot Book" is an introduction to this rich theory, starting with our familiar understanding of knots and a bit of...
World Scientific Publ., 1999. — 409 p. — (Knots and Everything 20). — ISBN: 9810238789. One of the most significant unsolved problems in mathematics is the complete classification of knots. The main purpose of this book is to introduce the reader to the use of computer programming to obtain the table of knots. The author presents this problem as clearly and methodically as...
Cambridge University Press 1990. — 84 p. These lecture notes are an expanded version of the series of lectures I gave, by invitation of the Accademia Nazionale dei Lincei, at the University of Florence in November 1988. They have also benefited from the seminar I ran in Oxford during that Autumn term. I am grateful in particular to Graeme Segal, Nigel Hitchin and Ruth Lawrence...
World Sci.Publ., 1995. — 188 p. — (Series on Knots and Everything 09). — ISBN 9810222122. The authors aim to reinstate a spirit of philosophical enquiry in physics. They abandon the intuitive continuum concepts and build up constructively a combinatorial mathematics of process. This radical change alone makes it possible to calculate the coupling constants of the fundamental...
Princeton University Press, 1974. — 230 p. Braid Groups Definition of the braid groups Configuration spaces Braid groups of manifolds Braid group of the plane Braid group of the sphere Survey of 2-manifold braid groups Braids and Links Closed braids and links Markov's theorem The conjugacy problems in Artin's braid group The algebraic link problem Magnus Representations Free...
Germany: de Gruyter, 2018. — 200 p. — ISBN: 311057148X. The aim of this book is to present recent results in both theoretical and applied knot theory which are at the same time stimulating for leading researchers in the field as well as accessible to non-experts. The book comprises recent research results while covering a wide range of different sub-disciplines, such as the...
Germany: de Gruyter, 2018. — 299 p. — ISBN 978-3-11-057148-6. The aim of this book is to present recent results in both theoretical and applied knot theory which are at the same time stimulating for leading researchers in the field as well as accessible to non-experts. The book comprises recent research results while covering a wide range of different sub-disciplines, such as...
Second Revised and Extended Edition, Walter de Gruyter; Berlin · New York 2003 1 Knots and Isotopies A Knots B Equivalence of Knots C Knot Projections D Global Geometric Properties E History and Sources F Exercises 2 Geometric Concepts A Geometric Properties of Projections B Seifert Surfaces and Genus C Companion Knots and Product Knots D Braids, Bridges, Plats E Slice Knots...
Berlin-New York: Walter de Gruyter, 2003. — 573 p. — ISBN: 3-11-017005-1. This book is an introduction to classical knot theory . Topics covered include: different constructions of knots, knot diagrams, knot groups, fibred knots, characterisation of torus knots, prime decomposition of knots, cyclic coverings and Alexander polynomials and modules together with the free...
World Scientific Publishing Co. Pte. Ltd., 2005. — 640 p. — (Series on Knots and Everything 36). — ISBN: 9812561870. The physical properties of knotted and linked configurations in space have long been of interest to mathematicians. More recently, these properties have become significant to biologists, physicists, and engineers among others. Their depth of importance and...
Ambridge University Press, 2004. — 344 p. — ISBN: 0521548314. Knots and links are studied by mathematicians, and are also finding increasing application in chemistry and biology. Many naturally occurring questions are often simple to state, yet finding the answers may require ideas from the forefront of research. This readable and richly illustrated 2004 book explores selected...
Cambridge University Press, 2004. — 344 p. — ISBN13: 978-0521548311, ISBN10: 0521548314 Knots and links are studied by mathematicians, and are also finding increasing application in chemistry and biology. Many naturally occurring questions are often simple to state, yet finding the answers may require ideas from the forefront of research. This readable and richly illustrated...
Springer, 1963. — 189 p. Knot theory is a kind of geometry, and one whose appeal is very direct because the objects studied are perceivable and tangible in everyday physical space. It is a meeting ground of such diverse branches of mathematics as group theory, matrix theory, number theory, algebraic geometry, and differential geometry, to name some of the more prominent ones....
Springer- Verlag, 1963. — 189 p. Prerequisites Knots and Knot Types The Fundamental Group The Free Groups Presentation of Groups Calculation of Fundamental Groups Presentation of a Knot Group The Free Calculus and the Elementary Ideals The Knot Polynomials Characteristic Properties of the Knot Polynomials Appendix Differentiable Knots are Tame Appendix Categories and groupoids...
New York: Chapman and Hall/CRC, 2016. — 284 p. The Only Undergraduate Textbook to Teach Both Classical and Virtual Knot Theory. An Invitation to Knot Theory: Virtual and Classical gives advanced undergraduate students a gentle introduction to the field of virtual knot theory and mathematical research. It provides the foundation for students to research knot theory and read journal...
New York: Chapman and Hall/CRC, 2016. — 284 p. — ISBN13: 978-1-4987-0164-8. The Only Undergraduate Textbook to Teach Both Classical and Virtual Knot Theory. An Invitation to Knot Theory: Virtual and Classical gives advanced undergraduate students a gentle introduction to the field of virtual knot theory and mathematical research. It provides the foundation for students to...
Princeton University Press, 2011. — 458 p. The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text...
World Scientific Publishing Company, 2024. — 508 p. A classic knot is an embedded simple loop in 3-dimensional space. It can be described as a 4-valent planar graph or network in the horizontal plane, with the vertices or crossings corresponding to double points of a projection. At this stage we have the shadow of the knot defined by the projection. We can reconstruct the knot...
Singapore: World Scientific Publishing Company, 2012. — 363 p. This book serves as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors. It emphasizes the features of the multicomponent case not normally considered by knot-theorists, such as longitudes, the homological complexity of many-variable Laurent polynomial...
Springer, 2018. — ix+120 p. — (Springer Briefs in Mathematical Physics, 30). — ISBN: 978-981-13-1150-5. The volume conjecture fascinated not only knot theorists but also physicists. The aim of this book is to study the volume conjecture from a mathematical viewpoint. The volume conjecture states that a certain limit of the colored Jones polynomial of a knot in the...
CRC Press, Taylor & Francis Group, 2016. — 221 p. — ISBN: 1498736750. Knot Projections offers a comprehensive overview of the latest methods in the study of this branch of topology, based on current research inspired by Arnold’s theory of plane curves, Viro’s quantization of the Arnold invariant, and Vassiliev’s theory of knots, among others. The presentation exploits the...
New York: Dover Publications, 2017. — 154 p. - (Aurora: Dover Modern Math Originals) This book does not follow the design of a traditional math textbook. There are very few complete proofs included, and the exercises are not listed at the end of each section. Instead, this text is an invitation to ponder, question, create, and figure out on your own some beautiful mathematical...
New York, USA: Dover Publ., Inc., 2017. — 172 p. — ISBN: 0486804631. This well-written and engaging volume, intended for undergraduates, introduces knot theory, an area of growing interest in contemporary mathematics. The hands-on approach features many exercises to be completed by readers. Prerequisites are only a basic familiarity with linear algebra and a willingness to...
Princeton University Press, 1983. — 170 p. — ISBN: 0-691-08336-3. This exploration of combinatorics and knot theory is geared toward advanced undergraduates and graduate students. The author draws upon his work as a topologist to illustrate the relationships between knot theory and statistical mechanics, quantum theory, and algebra, as well as the role of knot theory in...
Princeton University Press, 1983. — 170 p. — ISBN: 0-691-08336-3. This exploration of combinatorics and knot theory is geared toward advanced undergraduates and graduate students. The author draws upon his work as a topologist to illustrate the relationships between knot theory and statistical mechanics, quantum theory, and algebra, as well as the role of knot theory in...
Язык узловых диаграмм оказывается полезным для представления нестандартных множеств и формальной комбинаторной логики. Sets, knots, recursions Knot set theory Arrow Epistemology Lambda calculus and topology Interlock algebra The LD-Magma On Godel's Theorem Quantum Knots and Topological Quantum Field Theory Knot and circuits Logic and circuit design - Knot Automata Pregeometry
University of Illinois, Chicago. — 1984. — 82 p. This essay constitutes an introduction to the theory of knots as it has been influenced by developments concurrent with the discovery of the Jones polynomial in 1984 and the subsequent explosion of research that followed this signal event in the mathematics of the twentieth century. I hope to give the flavor of these...
4th Edition. — World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, USA, 2013. — 866 p. — (Series on Knots and Everything 53). — ISBN: 9814383007. This invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that...
4th Edition. – World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, USA, 2013. – 866 p. – ISBN: 9814383007, 9814383015 This invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes...
Birkhäuser, 1990. — 427 pp. This book is an expanded English version of "Knot Theory" which I edited and which was published in the original Japanese by Springer-Verlag Tokyo in 1990. This version covers many research methods and results of knot theory in classical dimensions which were developed before 1995. The purpose is to inform advanced undergraduates and graduate...
World Scientific, 1990. — 476 p. — (Advanced Series in Mathematical Physics, Vol. 11). The book gives a comprehensive and full account of recent developments and deep interrelations of new results in modern mathematical physics and will be useful for all scholars aiming to enter quickly into this new and promising field of science. Preface. Pioneering works on new knot...
Springer, 1997. — 213 p. — (Graduate Texts in Mathematics 175). — ISBN: 978-1-4612-6869-7. This account is an introduction to mathematical knot theory, the theory of knots and links of simple closed curves in three-dimensional space. Knots can be studied at many levels and from many points of view. They can be admired as artifacts of the decorative arts and crafts, or viewed as...
Washington: MAA, 1993. — 254 p. Acknowledgements A Ccentury of Knot Theory Whai is a Knot? Wild Knots and Unknottings The Definition of a Knot Equivalence of Knots, Deformations Diagrams and Projections Orientations Combinatorial Techniques Reidemeister Moves Colorings A Generalization of Colorability, mod p Labelings Matrices, Labelings, and Determinants The Alexander...
Boca Raton: CRC Press, 2018. — 581 p. Over the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and alge-bra. It suffices to mention the great progress in knot homology theory (Khovanov homology and Ozsvath-Szabo Heegaard-Floer homology), the A-polynomial which give rise to strong...
Elsevier, 2005. — 503 p. — ISBN10: 044451452X, ISBN13: 978-0444514523 This book is a survey of current topics in the mathematical theory of knots. For a mathematician, a knot is a closed loop in 3-dimensional space: imagine knotting an extension cord and then closing it up by inserting its plug into its outlet. Knot theory is of central importance in pure and applied...
Elsevier, 2005. — 503 p. — ISBN: 0-444-51452-X. This book is a survey of current topics in the mathematical theory of knots. For a mathematician, a knot is a closed loop in 3-dimensional space: imagine knotting an extension cord and then closing it up by inserting its plug into its outlet. Knot theory is of central importance in pure and applied mathematics, as it stands at a...
European Mathematical Society, 2017. — 146 p. — (EMS Series of Lectures in Mathematics) — ISBN: 3037191805. Michel Kervaire wrote six papers which can be considered fundamental to the development of higher-dimensional knot theory. They are not only of historical interest but naturally introduce to some of the essential techniques in this fascinating theory. This book is written...
World Scientific Publishing Co. Pte Ltd. 1994. — 208 p. — ISBN10: 9810220057, ISBN13: 978-9810220051 This volume includes both rigorous asymptotic results on the inevitability of random knotting and linking, and Monte Carlo simulations of knot probability at small lengths. The statistical mechanics and topology of surfaces on the d-dimensional simple cubic lattice are...
Birkhäuser, 1996. — 349 pp. Knots and braids have been extremely beneficial through the ages to our actual existence and progress. For example, in the primordial ages of our existence, in order to construct an axe a piece of stone was bound/knotted to a sturdy piece of wood. To make a net, vines or creepers, animal hair, et cetera were bound/braided together. Also it is known...
Birkhäuser, 1996. — 349 p. — ISBN13: 978-0-8176-3817-2. Теория узлов-это понятие в алгебраической топологии, которое нашло применение в различных математических задачах, а также в задачах информатики, биологических и медицинских исследований и математической физики. Эта книга адресована широкой аудитории исследователей, начинающих аспирантов и студентов старших курсов в этих...
American Mathematical Society, 2020. — 392 p. — (Graduate Studies in Mathematics, 209). — ISBN 978-1470454999. This book provides an introduction to hyperbolic geometry in dimension three, with motivation and applications arising from knot theory. Hyperbolic geometry was first used as a tool to study knots by Riley and then Thurston in the 1970s. By the 1980s, combining work of...
World Scientific Pub. Co Inc., 2008. — 272 p. — (Knots and everything 18). — ISBN: 978-981-277-173-5, ASIN 981-277-173-5. This unique book offers an original way of thinking about two of the most significant problems confronting modern theoretical physics: the unification of the forces of nature and the evolution of the universe. In bringing out the inadequacies of the...
World Scientific Publishing Co. Pte. Ltd. P O Box 128, Farrer Road, Singapore, 1998. — 426 p. — ISBN: 9810235305. In this book, experts in different fields of mathematics, physics, chemistry and biology present unique forms of knots which satisfy certain preassigned criteria relevant to a given field. They discuss the shapes of knotted magnetic flux lines, the forms of knotted...
World Scientific Publishing Co. Pte. Ltd. P O Box 128, Farrer Road, Singapore. – 1998. 426 Pages. –ISBN: 9810235305. In this book, experts in different fields of mathematics, physics, chemistry and biology present unique forms of knots which satisfy certain preassigned criteria relevant to a given field. They discuss the shapes of knotted magnetic flux lines, the forms of...
Walter de Gruyter GmbH & Co. KG, Berlin/New York, 2010. — 605 p. In this monograph we focus our attention on the topological aspects of the theory. Our goal is the construction and study of invariants of knots and 3-manifolds. There are several possible approaches to these invariants, based on Chern-Simons field theory, 2-dimensional conformal field theory, and quantum groups....
World Scientific, 1994. — 392 p. — (Advanced Series in Mathematical Physics 17). — ISBN 981021524X. The present volume is an updated version of the book edited by C N Yang and M L Ge on the topics of braid groups and knot theory, which are related to statistical mechanics. This book is based on the 1989 volume but has new material included and new contributors. On the...
Singapore: World Scientific, 2001. — 238 p. An exposition of building blocks for deformation theory of braided monoidal categories, giving rise to sequences of Vasseliv invariants of framed links, clarifying the interrelations between them.
Перевод с англ. В.Н. Лексина и И.Г. Щербак. — Предисловие В.И. Арнольда. — М.: Мир, 1995. — 192 с.: ил. — ISBN 5-03-002892-7. Основу небольшой книги известного английского математика составляют недавние работы Э. Виттена, связывающие открытые В. Джонсом полиномиальные инварианты узлов с топологической квантовой теорией поля. Основное внимание уделяется разъяснению идей и...
Перевод с англ. В.Н. Лексина и И.Г. Щербак. — Предисловие В.И. Арнольда. — М.: Мир, 1995. — 192 с.: ил. — ISBN 5-03-002892-7. Основу небольшой книги известного английского математика составляют недавние работы Э. Виттена, связывающие открытые В. Джонсом полиномиальные инварианты узлов с топологической квантовой теорией поля. Основное внимание уделяется разъяснению идей и...
Перевод с англ. А.М. Виноградова. — М.: Мир, 1967. — 348 с. Книга посвящена теории узлов, одной из ветвей алгебраической топологии, отличающейся своеобразной красотой и наглядностью, а также связями с другими разделами математики. В данном издании к основному тексту книги, задуманной как учебник по теории узлов, добавлены переводы обзорной статьи по теории узлов Р. Фокса и его...
Перевод с англ. А.М. Виноградова. — М.: Мир, 1967. — 348 с. Книга посвящена теории узлов, одной из ветвей алгебраической топологии, отличающейся своеобразной красотой и наглядностью, а также связями с другими разделами математики. В данном издании к основному тексту книги, задуманной как учебник по теории узлов, добавлены переводы обзорной статьи по теории узлов Р. Фокса и его...
М.: Эдиториал УРСС, 2001. — 304 c.
В книге изложены как классические результаты теории узлов, так и знаменитые и замечательные новейшие идеи последних лет, обуславливающий бурное развитие этой теории (полином Джонса, Кауфмана, HOMFLY, интеграл Концевича, теория Бар-Натана, теория кос, теорема Маркова, алгоритм Деорнуа, теория виртуальных узлов). Отдельно изложен авторский...
М.: Эдиториал УРСС, 2001. — 304 c. — ISBN: 5-8360-0287-8. В книге изложены как классические результаты теории узлов, так и знаменитые и замечательные новейшие идеи последних лет, обуславливающий бурное развитие этой теории (полином Джонса, Кауфмана, HOMFLY, интеграл Концевича, теория Бар-Натана, теория кос, теорема Маркова, алгоритм Деорнуа, теория виртуальных узлов). Отдельно...
Москва-Ижевск: Институт компьютерных исследований, 2005. — 512 с. Теория узлов играет видную роль в современной математике. Наиболее яркие результаты в этой теории были получены в последние несколько десятилетий. Одним из важных открытий в теории узлов является предложенная Луисом Кауфманом в 1996 году теория виртуальных узлов. Настоящая монография посвящена современному...
Москва-Ижевск: Институт компьютерных исследований, 2005. — 512 с.
Настоящая монография покрывает почти все направления и методы современной теории узлов. Изложение является замкнутым, поэтому книгу можно использовать для изучения узлов с самого начала. Особенное место в книге уделено бурно развивающейся в последнее время теории виртуальных узлов, а также авторскому подходу к...
М.: МЦНМО, 1997. — 352 с. — ISBN: 5-900916-10-3. Эта книга, прежде всего, - введение в замечательные результаты Вогана Джонса и Виктора Васильева об инвариантах узлов и зацеплений и в новые модификации этих инвариантов, включая математическое обоснование инвариантов Джойса-Виттена. Особое внимание уделяется геометрическим аспектам теории. Обсуждаются такие темы, как косы,...
М.: МЦНМО, 1997. — 352 с. Эта книга, прежде всего, - введение в замечательные результаты Вогана Джонса и Виктора Васильева об инвариантах узлов и зацеплений и в новые модификации этих инвариантов, включая математическое обоснование инвариантов Джойса-Виттена. Особое внимание уделяется геометрическим аспектам теории. Обсуждаются такие темы, как косы, гомеоморфизмы поверхностей,...
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