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Configuration spaces and Vassiliev classes in any dimension

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

math.GTarXiv:math/9910139

Abstract

The real cohomology of the space of imbeddings of S1 into Rn, 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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