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2002 Configuration spaces and Vassiliev classes in any dimension
Alberto S Cattaneo, Paolo Cotta-Ramusino, Riccardo Longoni
Algebr. Geom. Topol. 2(2): 949-1000 (2002). DOI: 10.2140/agt.2002.2.949

Abstract

The real cohomology of the space of imbeddings of S1 into 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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Alberto S Cattaneo. Paolo Cotta-Ramusino. Riccardo Longoni. "Configuration spaces and Vassiliev classes in any dimension." Algebr. Geom. Topol. 2 (2) 949 - 1000, 2002. https://doi.org/10.2140/agt.2002.2.949

Information

Received: 2 August 2002; Accepted: 12 October 2002; Published: 2002
First available in Project Euclid: 21 December 2017

zbMATH: 1029.57009
MathSciNet: MR1936977
Digital Object Identifier: 10.2140/agt.2002.2.949

Subjects:
Primary: 58D10
Secondary: 55R80, 81Q30

Rights: Copyright © 2002 Mathematical Sciences Publishers

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