Lie algebras and the (co)homology of configuration spaces

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences 2026 Open access

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Authors: Ben Knudsen
DOI: 10.1098/rsta.2024.0402
Cited by: 0

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'.

Fields of Study & Subjects

Advanced Topics in Algebra Homotopy and Cohomology in Algebraic Topology

Publication details

Journal / source
Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences
Volume
384
Issue
2328
Publication date
28 August 2026
Language
EN