Koszul duality factorization algebra topological chiral homology topological quantum field theory higher Morita category
Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 41, No 4, (2015), 369p-414p
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 . 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.