AN A∞ VERSION OF THE POINCARE LEMMA

We prove a categorified version of the Poincare lemma. The natural setting for our result is that of infinity-local systems. More precisely, we show that any smooth homotopy between maps f and g induces an A(infinity)-natural transformation between the corresponding pullback functors. This transformation is explicitly defined in terms of Chen's iterated integrals. In particular, we show that a homotopy equivalence induces a quasiequivalence on the DG categories of infinity-local system.