## Configuration spaces and Vassiliev classes in any dimension

by
Alberto S. Cattaneo
,
Paolo Cotta-ramusino
,
Riccardo Longoni

Citations: | 41 - 5 self |

### BibTeX

@MISC{Cattaneo_configurationspaces,

author = {Alberto S. Cattaneo and Paolo Cotta-ramusino and Riccardo Longoni},

title = {Configuration spaces and Vassiliev classes in any dimension},

year = {}

}

### OpenURL

### Abstract

Abstract. The real cohomology of the space of imbeddings of S 1 into R n, n> 3, is studied both by using configuration space integrals and by considering the restriction of classes defined on the corresponding spaces of immersions. Nontrivial classes are explicitly constructed. The cohomology classes obtained by configuration space integrals generalize in a nontrivial way the Vassiliev knot invariants obtained in three dimensions from the Chern–Simons perturbation theory. 1.