Configuration spaces and Vassiliev classes in any dimension

Alberto S. Cattaneo; Paolo Cotta-Ramusino; Riccardo Longoni

doi:10.2140/agt.2002.2.949

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Configuration spaces and Vassiliev classes in any dimension

Alberto S. Cattaneo·Paolo Cotta-Ramusino·Riccardo Longoni

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Abstract

The real cohomology of the space of imbeddings of S^1 into R^n, n>3, is studied by using configuration space integrals. Nontrivial classes are explicitly constructed. As a by-product, we prove the nontriviality of certain cycles of imbeddings obtained by blowing up transversal double points in immersions. These cohomology classes generalize in a nontrivial way the Vassiliev knot invariants. Other nontrivial classes are constructed by considering the restriction of classes defined on the corresponding spaces of immersions.

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Alberto S. Cattaneo, Paolo Cotta-Ramusino, Riccardo Longoni. 1999-10-26. Configuration spaces and Vassiliev classes in any dimension. https://doi.org/10.2140/agt.2002.2.949

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