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Configuration spaces and Vassiliev classes in any dimension


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

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.

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
Dewey Decimal Classification: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:05 Apr 2016 13:25
Publisher:Mathematical Sciences Publishers
ISSN:1472-2739
Additional Information:© Copyright 2002 Mathematical Sciences Publishers
Publisher DOI:https://doi.org/10.2140/agt.2002.2.949
Permanent URL: https://doi.org/10.5167/uzh-21936

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