Twisting cochains and duality between minimal algebras and minimal Lie algebras

Hain, Richard M.

doi:10.1090/S0002-9947-1983-0690059-3

Twisting cochains and duality between minimal algebras and minimal Lie algebras
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Trans. Amer. Math. Soc. 277 (1983), 397-411 Request permission

Abstract:

An algebraic duality theory is developed between $1$-connected minimal cochain algebras of finite type and connected minimal chain Lie algebras of finite type by means of twisting cochains. The duality theory gives a concrete relationship between Sullivan’s minimal models, Chen’s power series connections and the various Lie algebra models of a $1$-connected topological space defined by Quillen, Allday, Baues-Lemaire and Neisendorfer. It can be used to compute the Lie algebra model of a space from the algebra model of the space and vice versa.

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