Configuration spaces and Vassiliev classes in any dimension

Details Configuration spaces and Vassiliev classes in any dimension Configuration spaces and Vassiliev classes in any dimension

1999-10-26

arxiv.org/abs/math/9910139v4

Algebr. Geom. Topol. 2 (2002) 949-1000

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-39.abs.html

Scientific paper

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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