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The first part discusses "pre-Vassiliev" knot theory, from knot arithmetics through the Jones polynomial and the famous Kauffman-Murasugi theorem. The fourth part describes a new way, proposed by the author, to encode knots by d-diagrams. The book is divided into six thematic sections.

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The first part discusses "pre-Vassiliev" knot theory, from knot arithmetics through the Jones polynomial and the famous Kauffman-Murasugi theorem. A section devoted to the Vassiliev knot invariants follows, wherein the author proves that Vassiliev invariants are stronger than all polynomial invariants and introduces Bar-Natan's theory on Lie algebra respresentations and knots. Part Five delves into virtual knot theory and virtualizations of knot and link invariants. The book concludes with an introduction to knots in 3-manifolds and Legendrian knots and links, including Chekanov's differential graded algebra DGA construction.

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This section includes the author's own important results regarding new invariants of virtual knots. The fourth part describes a new way, proposed by the author, to encode knots by d-diagrams. The book concludes with an introduction to knots in 3-manifolds and Legendrian knots and links, including Chekanov's differential graded algebra DGA construction.

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Part Five delves into virtual knot theory and virtualizations of knot and link invariants. Part Five delves into virtual knot theory and virtualizations of knot and link invariants. The first part discusses "pre-Vassiliev" knot theory, from knot arithmetics through the Jones polynomial and the famous Kauffman-Murasugi theorem.

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In a unique presentation with contents not found in any other monograph, Knot Theory describes, with full proofs, the main concepts and the latest investigations in the field. Knot Theory is notable not only for its expert presentation of knot theory's state of the art but also for its accessibility. The book is divided into six thematic sections. The fourth part describes a new way, proposed by the author, to encode knots by d-diagrams.

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Part Five delves into virtual knot theory and virtualizations of knot and link invariants. Knot Theory is notable not only for its expert presentation of knot theory's state of the art but also for its accessibility. This method allows the encoding of topological objects by words in a finite alphabet. The book is divided into six thematic sections.

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Part Five delves into virtual knot theory and virtualizations of knot and link invariants. The first part discusses "pre-Vassiliev" knot theory, from knot arithmetics through the Jones polynomial and the famous Kauffman-Murasugi theorem.

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This method allows the encoding of topological objects by words in a finite alphabet. The fourth part describes a new way, proposed by the author, to encode knots by d-diagrams.

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Posted in DEFAULT | 4 Comments »




4 Commentsto Pppppppppppppppppppppppppppppp

  1. Bahn says:

    This method allows the encoding of topological objects by words in a finite alphabet.

  2. Mauzilkree says:

    It is valuable as a professional reference and will serve equally well as a text for a course on knot theory. A section devoted to the Vassiliev knot invariants follows, wherein the author proves that Vassiliev invariants are stronger than all polynomial invariants and introduces Bar-Natan's theory on Lie algebra respresentations and knots.

  3. Tobei says:

    Part Five delves into virtual knot theory and virtualizations of knot and link invariants. It is valuable as a professional reference and will serve equally well as a text for a course on knot theory.

  4. Yogore says:

    The second part explores braid theory, including braids in different spaces and simple word recognition algorithms. The second part explores braid theory, including braids in different spaces and simple word recognition algorithms.

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