Generalized String Topology and Derived Koszul Duality

2013/06/28 by Aaron M Royer, Royer, Aaron M
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT

paper · pdf · doi:10.48550/arxiv.1306.6708

Comments welcome!

arxiv created 2013/06/28 · arxiv updated 2013/07/01

Abstract

The generalized string topology construction of Gruher and Salvatore assigns to any bundle of E_n-algebras A over a closed oriented manifold M a collection of intersection-type operations on the homology of the total space. These operations are realized by an H_n-ring structure on the Thom spectrum A^-TM under the Thom isomorphism. We rigidify and extend this construction to a functor connecting the homotopy theory of spaces and spectra parametrized by M to the homotopy theory of module spectra over the Atiyah-Milnor-Spanier-Whitehead dual M^-TM ≃ \bbD M. Then, using an ∞-categorical version of Morita theory, we give an alternative description of our construction in terms of the derived Koszul duality (alias bar-cobar duality) between Σ^∞₊ ΩM and \bbD M.

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