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OverviewThis work contains numerical isotopy invariants for knots in the product of a surface (not necessarily orientable) with a line and for links in 3-space. These invariants, called Gauss diagram invariants, are defined in a combinatorial way using knot diagrams. The natural notion of global knots is introduced. Global knots generalize closed braids. If the surface is not the disc or the sphere then there are Gauss diagram invariants which distinguish knots that cannot be distinguished by quantum invariants. There are specific Gauss diagram invariants of finite type for global knots. These invariants, called T-invariants, separate global knots of some classes and it is conjectured that they separate all global knots. T-invariants cannot be obtained from the (generalized) Kontsevich integral. The book is designed for research workers in low-dimensional topology. Full Product DetailsAuthor: T. FiedlerPublisher: Springer Imprint: Springer Edition: 2001 ed. Volume: 532 Dimensions: Width: 15.50cm , Height: 2.30cm , Length: 23.50cm Weight: 1.730kg ISBN: 9780792371120ISBN 10: 0792371127 Pages: 412 Publication Date: 31 August 2001 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of Contents1 The space of diagrams.- 2 Invariants of knots and links by Gauss sums.- 3 Applications.- 4 Global knot theory in F2 × ?.- 5 Isotopies with restricted cusp crossing for fronts with exactly two cusps of Legendre knots in ST*?2.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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