Configuration spaces and Vassiliev classes in any dimension
Geometric Topology
2014-10-01 v4 High Energy Physics - Theory
Mathematical Physics
Algebraic Topology
math.MP
Quantum Algebra
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.
Cite
@article{arxiv.math/9910139,
title = {Configuration spaces and Vassiliev classes in any dimension},
author = {Alberto S. Cattaneo and Paolo Cotta-Ramusino and Riccardo Longoni},
journal= {arXiv preprint arXiv:math/9910139},
year = {2014}
}
Comments
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-39.abs.html