Poincaré/Koszul Duality

David Ayala; John Francis

doi:10.1007/s00220-019-03311-z

Poincaré/Koszul Duality

David Ayala, John Francis^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We prove a duality for factorization homology which generalizes both usual Poincaré duality for manifolds and Koszul duality for 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.

Original language	English (US)
Pages (from-to)	847-933
Number of pages	87
Journal	Communications in Mathematical Physics
Volume	365
Issue number	3
DOIs	https://doi.org/10.1007/s00220-019-03311-z
State	Published - Feb 7 2019

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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title = "Poincar{\'e}/Koszul Duality",

abstract = " We prove a duality for factorization homology which generalizes both usual Poincar{\'e} duality for manifolds and Koszul duality for 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. ",

author = "David Ayala and John Francis",

note = "Funding Information: 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. Publisher Copyright: {\textcopyright} 2019, Springer-Verlag GmbH Germany, part of Springer Nature.",

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doi = "10.1007/s00220-019-03311-z",

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AU - Ayala, David

AU - Francis, John

N1 - Funding Information: 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. Publisher Copyright: © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2019/2/7

Y1 - 2019/2/7

N2 - We prove a duality for factorization homology which generalizes both usual Poincaré duality for manifolds and Koszul duality for 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.

AB - We prove a duality for factorization homology which generalizes both usual Poincaré duality for manifolds and Koszul duality for 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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JO - Communications in Mathematical Physics

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ER -

Poincaré/Koszul Duality

Abstract

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