A model for configuration spaces of points

Ricardo Campos; Thomas Willwacher

A model for configuration spaces of points

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arxiv 1604.02043 v4 pith:2YYEVJAB submitted 2016-04-07 math.QA

Ricardo Campos , Thomas Willwacher This is my paper · ORCID

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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
math.AT 2025-05 conditional novelty 7.0 of 10

Configuration space integrals produce characteristic classes of framed fibre bundles with closed manifold fibres, generalizing Kontsevich's graph complex classes to arbitrary closed fibres.

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