The Atiyah–Sutcliffe conjecture and En algebras
Abstract
We show that a certain conjecture by Atiyah and Sutcliffe implies the existence of an E3-algebra (respectively E2-algebra) structure on the disjoint union of all complex (respectively real) full flag manifolds modulo symmetric groups. Moreover, we show that these structures are liftings of exotic E3 (respectively E2) structures on the free E∞-algebras on BU(1)+ (respectively BO(1)+), that do not extend to E4 (respectively E3) structures. We also provide some (co)homological calculations supporting the conjecture. This article is part of the theme issue 'Derived Lie algebras in geometry and topology'.
Fields of Study & Subjects
Advanced Algebra and Logic
Advanced Topics in Algebra
Advanced Operator Algebra Research
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