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Poincaré/Koszul Duality

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Abstract

We prove a duality for factorization homology which generalizes both usual Poincaré duality for manifolds and Koszul duality for \({\mathcal{E}_n}\)-algebras. The duality has application to the Hochschild homology of associative algebras and enveloping algebras of Lie algebras. We interpret our result at the level of topological quantum field theory.

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Acknowledgments

Our collaboration began at a workshop in Glanon in 2011. We are grateful to people of Glanon for their warm hospitality in hosting this annual workshop, and to Grégory Ginot for inviting us to participate in it. We have learned an enormous amount from Jacob Lurie; we use, in particular, his opuses [Lu1] and [Lu2] throughout. We thank Greg Arone for several very helpful conversations on Goodwillie calculus. JF thanks Kevin Costello for offering many insights in many conversations over the years. We thank the referees for their informed and detailed readings, which have significantly improved this paper.

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Authors and Affiliations

  1. Department of Mathematics, Montana State University, Bozeman, MT, 59717, USA

    David Ayala

  2. Department of Mathematics, Northwestern University, Evanston, IL, 60208, USA

    John Francis

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  1. David Ayala
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Correspondence to John Francis.

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Communicated by Y. Kawahigashi

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DA was partially supported by ERC adv. Grant No. 228082, and by the National Science Foundation under Awards 0902639 and 1507704. JF was supported by the National Science Foundation under Awards 1207758 and 1508040.

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Ayala, D., Francis, J. Poincaré/Koszul Duality. Commun. Math. Phys. 365, 847–933 (2019). https://doi.org/10.1007/s00220-019-03311-z

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