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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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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|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Uncontrolled Keywords:||configuration spaces, Vassiliev invariants, de Rham cohomology of spaces of imbeddings,immersions, Chen's iterated integrals, graph cohomology|
|Deposited On:||27 Jan 2010 12:24|
|Last Modified:||23 Nov 2012 16:08|
|Publisher:||Mathematical Sciences Publishers|
|Additional Information:||© Copyright 2002 Mathematical Sciences Publishers|
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