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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Twisting cochains and duality between minimal algebras and minimal Lie algebras

Author: Richard M. Hain
Journal: Trans. Amer. Math. Soc. 277 (1983), 397-411
MSC: Primary 55P62; Secondary 55U30
MathSciNet review: 690059
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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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Keywords: Minimal algebra, minimal Lie algebra, formal homology connection
Article copyright: © Copyright 1983 American Mathematical Society