Rational Homotopy Theory

Abstract

This is a survey of Rational Homotopy Theory, intended for a Mathematical Physics readership.

20 pages. In the version updated upon publication, material on the nerve of an $L_{\infty }$-algebra is added, along with some minor updates

References in corpus (14)

• Lie theory for nilpotent L-infinity algebras
• Rational sphere valued supercocycles in M-theory and type IIA string theory
• Twisted Cohomotopy implies M-theory anomaly cancellation on 8-manifolds
• The WZW term of the M5-brane and differential cohomotopy
• Framed M-branes, corners, and topological invariants
• The Rational Higher Structure of M-theory
• Twisted Cohomotopy implies level quantization of the full 6d Wess-Zumino term of the M5-brane
• Gauge enhancement of super M-branes via parametrized stable homotopy theory
• T-Duality from super Lie n-algebra cocycles for super p-branes
• Differential cohomotopy versus differential cohomology for M-theory and differential lifts of Postnikov towers
• Higher order Whitehead products and $L_{\infty }$ structures on the homology of a DGL
• Flux Quantization on Phase Space
• Variations of rational higher tangential structures
• Topological actions via gauge variations of higher structures

Cited by in corpus (2)

• The Atiyah-Bott formula and connectivity in chiral Koszul duality
• Mysterious Triality and the Exceptional Symmetry of Loop Spaces