Nontrivial classes in $H^*(Imb(S^1,\R^n))$ from nontrivalent graph cocycles

Details Nontrivial classes in $H^*(Imb(S^1,\R^n))$ from nontrivalent graph cocycles Nontrivial classes in $H^*(Imb(S^1,\R^n))$ from nontrivalent graph cocycles

2004-04-09

arxiv.org/abs/math/0404196v2

Mathematics

Geometric Topology

10 pages, 11 figures. V2: minor changes, typos corrected

Scientific paper

We construct nontrivial cohomology classes of the space $Imb(S^1,\R^n)$ of imbeddings of the circle into $\R^n$, by means of Feynman diagrams. More precisely, starting from a suitable linear combination of nontrivalent diagrams, we construct, for every even number $n\geq 4$, a de Rham cohomology class on $Imb(S^1,\R^n)$. We prove nontriviality of these classes by evaluation on the dual cycles.

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