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Title: Koszul Duality for Locally Constant Factorization Algebras
Authors: Matsuoka, Takuo
Keywords: Koszul duality
factorization algebra
topological chiral homology
topological quantum field theory
higher Morita category
Issue Date: 2015
Publisher: Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 41, No 4, (2015), 369p-414p
Abstract: Generalizing Jacob Lurie’s idea on the relation between the Verdier duality and the iterated loop space theory, we study the Koszul duality for locally constant factorization algebras. We formulate an analogue of Lurie’s “nonabelian Poincaré duality” theorem (which is closely related to earlier results of Graeme Segal, of Dusa McDuff, and of Paolo Salvatore) in a symmetric monoidal stable infinity 1-category carefully, using John Francis’ notion of excision. Its proof depends on our study of the Koszul duality for En-algebras in [12]. As a consequence, we obtain a Verdier type equivalence for factorization algebras by a Koszul duality construction. 2010 Mathematics Subject Classification: 55M05, 16E40, 57R56, 16D90.
ISSN: 1310-6600
Appears in Collections:Volume 41, Number 4

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