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Polynomial One-cocycles for Knots and Closed Braids : Series On Knots And Everything : Book 64 - Thomas Fiedler

Polynomial One-cocycles for Knots and Closed Braids

By: Thomas Fiedler

eText | 27 August 2019

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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:
  • Introduction
  • 1-cocycles for Classical Knots
  • A 1-cocycle for All Knots and All Loops in the Solid Torus
  • Polynomial 1-cocycles for Closed Braids in the Solid Torus

Readership: Graduate students and researchers.Low Dimensional Topology;Knot Theory;Diagrammatic 1-Cocycles;Tetrahedron Equation;Conjugacy Classes of Braids00
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Non-FictionMathematicsTopologyGeometryAlgebraic Geometry

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