Koszul duality in algebraic topology (Q1946122)

The author first gives a brief survey of the occurrence of Kozul duality of operads in various classical contexts; in particular, Kozul-Moore duality between the bar and co-bar constructions, and the Lie-algebraic version due to Quillen, one of the cornerstones of Quillen's work on rational homotopy theory. The author concludes by connecting this classical framework with his results on the Hopf-invariant map appearing in recent joint work with \textit{B. Walter} [Trans. Am. Math. Soc. 365, No. 2, 861--883 (2013; Zbl 1275.55007)].