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Configuration spaces and
Vassiliev classes in any dimension
Alberto S Cattaneo, Paolo Cotta-Ramusino and Riccardo Longoni |
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Algebraic & Geometric Topology 2 (2002) 949–1000
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arXiv: math.GT/9910139 |
Abstract |
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The real cohomology of the space of imbeddings of into , , 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. |
Keywords
configuration spaces, Vassiliev invariants, de Rham
cohomology of spaces of imbeddings, immersions, Chen's
iterated integrals, graph cohomology
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Mathematical Subject Classification 2000
Primary: 58D10
Secondary: 55R80, 81Q30
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References |
Forward citations |
Publication
Received: 2 August 2002
Accepted: 12 October 2002
Published: 25 October 2002
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Authors |
| Alberto S Cattaneo | |
| Mathematisches Institut Universität Zürich–Irchel Winterthurerstrasse 190 CH-8057 Zürich Switzerland |
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| Paolo Cotta-Ramusino | |
| Dipartimento di Fisica Università degli Studi di Milano & INFN Sezione di Milano Via Celoria, 16 I-20133 Milano Italy |
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| Riccardo Longoni | |
| Dipartimento di Matematica “G.
Castelnuovo” Università di Roma “La Sapienza” Piazzale Aldo Moro, 5 I-00185 Roma Italy |
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