Calculus of the first non-trivial 1-cocycle of the space of long knots
نویسنده
چکیده
For the space of long knots in R, 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, given in [1], and find the value mod2 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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