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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21936

Cattaneo, A S; Cotta-Ramusino, P; Longoni, R (2002). Configuration spaces and Vassiliev classes in any dimension. Algebraic & Geometric Topology, 2:949-1000 (electronic).

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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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
DDC:510 Mathematics
Uncontrolled Keywords:configuration spaces, Vassiliev invariants, de Rham cohomology of spaces of imbeddings,immersions, Chen's iterated integrals, graph cohomology
Language:English
Date:2002
Deposited On:27 Jan 2010 12:24
Last Modified:23 Nov 2012 16:08
Publisher:Mathematical Sciences Publishers
ISSN:1472-2739
Additional Information:© Copyright 2002 Mathematical Sciences Publishers
Publisher DOI:10.2140/agt.2002.2.949

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