Calculating the first nontrivial 1-cocycle in the space of long knots |
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| Authors: | V Turchin |
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| Institution: | (1) Catholic University of Louvain, Moscow;(2) Independent University of Moscow, Moscow |
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| 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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| Keywords: | long knot Vassiliev invariant finite order cocycle Casson’ s invariant |
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