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Transactions of the American Mathematical Society

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



Intrinsic formality and certain types of algebras

Author: Gregory Lupton
Journal: Trans. Amer. Math. Soc. 319 (1990), 257-283
MSC: Primary 55P62; Secondary 32C10
MathSciNet review: 1005081
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Abstract: In this paper, a type of algebra is introduced and studied from a rational homotopy point of view, using differential graded Lie algebras. The main aim of the paper is to establish whether or not such an algebra is the rational cohomology algebra of a unique rational homotopy type of spaces. That is, in the language of rational homotopy, whether or not such an algebra is intrinsically formal. Examples are given which show that, in general, this is not so--7.8 and 7.9. However, whilst it is true that not all such algebras are intrinsically formal, some of them are. The main results of this paper show a certain class of these algebras to be intrinsically formal--Theorem $ 2$ (6.1); and a second, different type of algebra also to be intrinsically formal--Theorem $ 1$ (5.2), which type of algebra overlaps with the first type in many examples of interest. Examples are given in $ \S7$.

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Keywords: Rational homotopy, intrinsic formality, Kähler manifolds
Article copyright: © Copyright 1990 American Mathematical Society