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.

Configuration spaces and Vassiliev classes in any dimension / A. Cattaneo, P. Cotta-Ramusino, R. Longoni. - In: ALGEBRAIC AND GEOMETRIC TOPOLOGY. - ISSN 1472-2739. - 2(2002 Oct 25), pp. 949-1000.

Configuration spaces and Vassiliev classes in any dimension

P. Cotta-Ramusino;
2002-10-25

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.
Configuration spaces; Vassiliev invariants; de Rham cohomology of spaces of imbeddings and immersions; Chen’s iterated integrals; graph cohomology
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
ALGEBRAIC AND GEOMETRIC TOPOLOGY
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/284877
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