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Configuration spaces and Vassiliev classes in any dimension | | Alberto S. Cattaneo
; Paolo Cotta-Ramusino
; Riccardo Longoni
; | | Date: |
26 Oct 1999 | | Journal: | Algebr. Geom. Topol. 2 (2002) 949-1000 | | Subject: | Geometric Topology; Algebraic Topology; Quantum Algebra MSC-class: 58D10, 55R80, 81Q30 | math.GT hep-th math-ph math.AT math.MP math.QA | | Abstract: | The real cohomology of the space of imbeddings of S^1 into R^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. | | Source: | arXiv, math.GT/9910139 | | Services: | Forum | Review | PDF | Favorites | |
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