Coloured Koszul duality and strongly homotopy operads

2003/12/07 by Pepijn van der Laan, van der Laan, Pepijn
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Quantum Algebra (math.QA) #math.AT #math.QA

paper · pdf · doi:10.48550/arxiv.math/0312147

17 pages, 4 figures. V2: minor corrections

arxiv created 2004/04/20 · arxiv updated 2009/12/01

Abstract

This paper proves Koszul duality for coloured operads and uses it to introduce strongly homotopy operads as a suitable homotopy invariant version of operads. It shows that rational chains on configuration spaces of points in the plane form a strongly homotopy operad quasi isomorphic to the chains on the little disks operad.

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• Koszul Operads Governing Props and Wheeled Props
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• Explicit Homotopy Equivalences Between Some Operads