Polynomial One-cocycles for Knots and Closed Braids
Traditionally, knot theory deals with diagrams of knots and the search of invariants of diagrams which are invariant under the well known Reidemeister moves. This book goes one step beyond: it gives a method to construct invariants for one parameter famillies of diagrams and which are invariant under 'higher' Reidemeister moves. Luckily, knots in 3-space, often called classical knots, can be transformed into knots in the solid torus without loss of information. It turns out that knots in the solid torus have a particular rich topological moduli space. It contains many 'canonical' loops to which the invariants for one parameter families can be applied, in order to get a new sort of invariants for classical knots.Contents: Introduction1-cocycles for Classical KnotsA 1-cocycle for All Knots and All Loops in the Solid TorusPolynomial 1-cocycles for Closed Braids in the Solid TorusReadership: Graduate students and researchers.Low Dimensional Topology;Knot Theory;Diagrammatic 1-Cocycles;Tetrahedron Equation;Conjugacy Classes of Braids00
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