One-cocycles And Knot Invariants
Book Details
Format
Hardback or Cased Book
Book Series
Series on Knots & Everything
ISBN-10
9811262993
ISBN-13
9789811262999
Publisher
World Scientific Publishing Co Pte Ltd
Imprint
World Scientific Publishing Co Pte Ltd
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Jan 31st, 2023
Print length
340 Pages
Weight
648 grams
Dimensions
15.70 x 23.60 x 2.60 cms
Product Classification:
Algebraic geometry
Ksh 21,600.00
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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.
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