Non-Formality of Planar Configuration Spaces in Characteristic 2

Abstract

AbstractWe prove that the ordered configuration space of four points or more in the plane has a nonformal singular cochain algebra in characteristic 2. This is proved by constructing an explicit nontrivial obstruction class in the Hochschild cohomology of the cohomology ring of the configuration space, by means of the Barratt–Eccles–Smith simplicial model. We also show that if the number of points does not exceed its dimension then a Euclidean configuration space is intrinsically formal over any ring.