2014/09/24 by Takuo Matsuoka, Matsuoka, Takuo · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AT #math.KT #math.QA #msc:16D90 #msc:16E40 #msc:55M05 #msc:57R56
paper · pdf · doi:10.48550/arxiv.1409.6945
32 pages. Section 2.0 slightly simplified, References updated. Comments welcome!
arxiv created 2015/03/12 · arxiv updated 2015/03/13
Generalising 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 factorisation algebras. We formulate an analogue of Lurie's "nonabelian Poincare 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 category carefully, using John Francis' notion of excision. Its proof depends on our earlier study of the Koszul duality for En-algebras. As a consequence, we obtain a Verdier type equivalence for factorisation algebras by a Koszul duality construction.