Configuration space integrals produce characteristic classes of framed fibre bundles with closed manifold fibres, generalizing Kontsevich's graph complex classes to arbitrary closed fibres.
A model for configuration spaces of points
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abstract
We construct a real combinatorial model for the configuration spaces of points of compact smooth oriented manifolds without boundary. We use these models to show that the real homotopy type of configuration spaces of a simply connected such manifold only depends on the real homotopy type of the manifold. Moreover, we show that for framed $D$-dimensional manifolds these models capture a natural right homotopy action of the little $D$-disks operad.
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Characteristic classes of framed fibre bundles
Configuration space integrals produce characteristic classes of framed fibre bundles with closed manifold fibres, generalizing Kontsevich's graph complex classes to arbitrary closed fibres.