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One-cocycles And Knot Invariants

Thomas Fiedler (Univ Paul Sabatier, France)

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Hardback

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English
World Scientific Publishing Co Pte Ltd
31 January 2023
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:  
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:  
Audience:   College/higher education ,  Professional and scholarly ,  Primary ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active

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