POLYNOMIAL ONE-COCYCLES FOR KNOTS AND CLOSED BRAIDS

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The book explores advanced knot theory by introducing a method for creating invariants for one-parameter families of knot diagrams, focusing on higher Reidemeister moves. It highlights the transformation of classical knots in 3-space into knots within a solid torus, preserving essential information. The solid torus's rich topological moduli space is examined, showcasing various "canonical" loops that facilitate the application of these new invariants, ultimately enriching the understanding of classical knots.