LinKnot - Knot Theory by Computer provides a unique view of selected topics in knot theory suitable for students, research mathematicians, and readers with backgrounds in other exact sciences, including chemistry, molecular biology and physics.The book covers basic notions in knot theory, as well as new methods for handling open problems such as unknotting number, braid family representatives, invertibility, amphicheirality, undetectability, non-algebraic tangles, polyhedral links, and (2,2)-moves.Hands-on computations using Mathematica or the webMathematica package LinKnot and beautiful illustrations facilitate better learning and understanding. LinKnot is also a powerful research tool for experimental mathematics implementation of Caudron's ideas. The use of Conway notation enables experimenting with large families of knots and links.Conjectures discussed in the book are explained at length. The beauty, universality and diversity of knot theory is illuminated through various non-standard applications: mirror curves, fullerens, self-referential systems, and KL automata.
Basic Graph Theory; Shadows of KLs; Notation of Knots and Links (KLs); Gauss and Dowker Code; KL Diagrams; Reidemeister Moves; Conway Notation; Classification of KLs; Chirality of KLs; Unlinking Number and Unlinking Gap; KLs with Unlinking Number One; Non-Invertible KLs; Braids; Braid Family Representatives; Borromean Links; Recognition and Generation of KLs; Polynomial Invariants; Experimenting with KLs; Derivation and Classification of KLs; Basic Polyhedra, Polyhedral KLs, and Non-Algebraic Tangles; Non-Alternating and Almost Alternating KLs; Families of Undetectable KLs; Detecting Chirality of KLs by Polynomial Invariants; History of Knot Theory and Its Applications; Mirror Curves; KLs and Fullerenes; KLs and Mathematical Logic; Self-Referential Systems; KL Automata.
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- ID: 9789812772237
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