Lie algebras and the (co)homology of configuration spaces

Abstract

We survey decades of research identifying the (co)homology of configuration spaces with Lie algebra (co)homology. The different routes to this one proto-theorem offer genuinely different explanations of its truth, and we attempt to convey some sense of the conceptual core of each perspective. We close with a list of problems. This article is part of the theme issue 'Derived Lie algebras in geometry and topology'.