Poincaré/Koszul Duality

  • David Ayala
  • John FrancisEmail author


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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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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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsMontana State UniversityBozemanUSA
  2. 2.Department of MathematicsNorthwestern UniversityEvanstonUSA

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