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Calculus of the first non-trivial 1-cocycle of the space of long knots

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arxiv math/0502518 v2 pith:Z6ZB3UJW submitted 2005-02-24 math.AT

Victor Tourtchine This is my paper · ORCID
classification math.AT
keywords knotscocyclelongspacecocyclesdimensionfinitefirst
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For the space of long knots in R^3, Vassiliev's theory defines the so called finite order cocycles. Zero degree cocycles are finite type knot invariants. The first non-trivial cocycle of positive dimension in the space of long knots has dimension one and order three. We apply Vassiliev's combinatorial formula, and find the value mod 2 of this cocycle on the 1-cycles that are obtained by dragging knots one along the other or by rotating around a fixed line.

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Cited by 1 Pith paper

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  1. A Fox-Neuwirth Basis for the Sinha Spectral Sequence

    math.AT 2025-05 conditional novelty 6.0 of 10

    The Sinha spectral sequence for long knot cohomology is isomorphic, from the first page on, to a spectral sequence built from Fox-Neuwirth trees, for every dimension and coefficient group.

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