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- DescriptionSince discovery of the Jones polymial, kt theory has enjoyed a virtual explosion of important results and w plays a significant role in modern mathematics. In a unique presentation with contents t found in any other mograph, Kt Theory describes, with full proofs, the main concepts and the latest investigations in the field. The book is divided into six thematic sections. The first part discusses pre-Vassiliev kt theory, from kt arithmetics through the Jones polymial and the famous Kauffman-Murasugi theorem. The second part explores braid theory, including braids in different spaces and simple word recognition algorithms. A section devoted to the Vassiliev kt invariants follows, wherein the author proves that Vassiliev invariants are stronger than all polymial invariants and introduces Bar-Natan's theory on Lie algebra respresentations and kts. The fourth part describes a new way, proposed by the author, to encode kts by d-diagrams. This method allows the encoding of topological objects by words in a finite alphabet. Part Five delves into virtual kt theory and virtualizations of kt and link invariants. This section includes the author's own important results regarding new invariants of virtual kts. The book concludes with an introduction to kts in 3-manifolds and Legendrian kts and links, including Chekav's differential graded algebra (DGA) construction. Kt Theory is table t only for its expert presentation of kt theory's state of the art but also for its accessibility. It is valuable as a professional reference and will serve equally well as a text for a course on kt theory.
- Author(s)Vassily Manturov
- PublisherTaylor & Francis Ltd
- Date of Publication24/02/2004
- Place of PublicationLondon
- Country of PublicationUnited Kingdom
- ImprintCRC Press
- Content Note249 black & white illustrations, 1 black & white tables
- Weight725 g
- Width156 mm
- Height234 mm
- Spine28 mm
- Format DetailsUnsewn / adhesive bound
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