Appears in collection : 2023 - T2 - WS1 - GAP XVIII: Homotopy algebras and higher structures

In previous work, Ib Madsen and I discovered some remarkable higher structure, governed by Kontsevich’s Lie graph complex, in the rational cohomology of automorphism groups of certain high dimensional manifolds, specifically the “generalized surfaces” #g(Sd × Sd) for d > 1. In this talk, I will report on some recent developments prompted by this discovery. In particular, I will present new structural results for spaces of self-homotopy equivalences of arbitrary simply connected Poincaré duality spaces that lead to a more conceptual explanation of this higher structure.