$L_{\infty }$ and $A_{\infty }$ structures: then and now

Abstract

Looking back over 55 years of higher homotopy structures, I reminisce as I recall the early days and ponder how they developed and how I now see them. From the history of $A_{\infty }$-structures and later of $L_{\infty }$ -structures and their progeny, I hope to highlight some old results which seem not to have garnered the attention they deserve as well as some tantalizing new connections.

Hopefully the penultimate draft Now 41 pages 2 figures Comments and suggestions still most welcome. Don't hesitate to suggest your own work

References in corpus (6)

• Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet
• n-ary algebras: a review with applications
• Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket
• On the Uniqueness of L${}_{\infty }$ bootstrap: Quasi-isomorphisms are Seiberg-Witten Maps
• Bootstrapping Non-commutative Gauge Theories from L${}_{\infty }$ algebras
• A-infinity structures and Massey products

Cited by in corpus (2)

• Slightly Broken Higher Spin Symmetry: General Structure of Correlators
• Higher curvature Bianchi identities, generalised geometry and $L_{\infty }$ algebras