Abstract
For spaces of knots in ℝ3, the Vassiliev theory defines the so-called cocycles of finite order. The zero-dimensional cocycles are finite-order invariants. The first nontrivial cocycle of positive dimension in the space of long knots is one-dimensional and is of order 3. We apply the combinatorial formula given by Vassiliev in his paper
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Turchin, V. Calculating the first nontrivial 1-cocycle in the space of long knots. Math Notes 80, 101–108 (2006). https://doi.org/10.1007/s11006-006-0113-8
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DOI: https://doi.org/10.1007/s11006-006-0113-8