One-Cocycles and Knot Invariants is about classical knots, i.e., smooth oriented knots in 3-space. It introduces discrete combinatorial analysis in knot theory in order to solve a global tetrahedron equation. This new technique is then used to construct combinatorial 1-cocycles in a certain moduli space of knot diagrams. The construction of the moduli space makes use of the meridian and the longitude of the knot. The combinatorial 1-cocycles are therefore lifts of the well-known Conway polynomial of knots, and they can be calculated in polynomial time. The 1-cocycles can distinguish loops consisting of knot diagrams in the moduli space up to homology. They give knot invariants when they are evaluated on canonical loops in the connected components of the moduli space. They are a first candidate for numerical knot invariants which can perhaps distinguish the orientation of knots.
By:
Thomas Fiedler (Univ Paul Sabatier France) Imprint: World Scientific Publishing Co Pte Ltd Country of Publication: Singapore Volume: 73 ISBN:9789811262999 ISBN 10: 9811262993 Series:Series on Knots & Everything Pages: 340 Publication Date:31 January 2023 Audience:
College/higher education
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Professional and scholarly
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Primary
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Undergraduate
Format:Hardback Publisher's Status: Active