Mathematical review synthesizes decades of proofs connecting configuration space topology to Lie algebra homology, highlighting distinct conceptual frameworks across geometry and derived algebra.
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'.
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Ben Knudsen (2026) studied this question.
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