Diffeomorphism-equivariant configuration spaces with twisted summable labels

Mr Hongyun Yon (The University of Oxford)

Frank Adams 1,

We construct the diffeomorphism-equivariant “scanning map” associated to the configuration spaces of manifolds with twisted partial summable labels.  We follow P.  Salvatore's idea of non-commutative summation using E_n-algebra label for n-dimensional ambient manifolds and generalise the idea into a twisted case such that each particle comes with a label lying in a bundle of E_n algebra. To make the setting twisted, we define a bundle of Fulton-MacPherson operads over a manifold M whose fibre is built within a corresponding tangent space of M. A natural action of the group of diffeomorphisms of M arises from it.

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